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Final Program and Abstracts

2015

Sponsored by the SIAM Activity Group on Dynamical Systems

The SIAM Activity Group on Dynamical Systems provides a forum for the exchange of ideas and information between mathematicians and applied scientists whose work involves dynamical systems. The goal of this group is to facilitate the development and application of new theory and methods of dynamical systems. The techniques in this area are making major contributions in many areas, including biology, nonlinear optics, fluids, chemistry, and mechanics. This activity group supports the web portal DSWeb, sponsors special sessions at SIAM meetings, organizes a biennial conference, and awards biennial prizes—the Jürgen Moser Lecture, J. D. Crawford Prize, and the Red Sock Award. The activity group also sponsors the DSWeb Student Competition for tutorials on dynamical systems and its applications written by graduate and undergraduate students and recent graduates. Members of SIAG/DS receive a complimentary subscription to the all-electronic, multimedia SIAM Journal on Applied Dynamical Systems.

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2 2015 SIAM Conference on Applications of Dynamical Systems

Table of Contents

Program-at-a-Glance ..... Separate handout

General Information .............................. 2

Get-togethers ......................................... 4

Featured Minisymposia ......................... 6

Minitutorials .......................................... 8

Invited Plenary Presentations ................ 9

Prize and Special Lecture ................... 11

Program Schedule ............................... 15

Poster Sessions ...........................57 & 71

Abstracts ............................................. 87

Speaker and Organizer Index ............ 233

Conference Budget ... Inside Back Cover

Hotel Meeting Room Map ... Back Cover

Organizing Committee Co-ChairsLora BillingsMontclair State University, USA

Panayotis KevrekidisUniversity of Massachusetts Amherst, USA

Organizing CommitteeChiara DaraioETH Zürich, Switzerland

Michelle GirvanUniversity of Maryland, USA

Jan MedlockOregon State University, USA

Igor MezicUniversity of California, Santa Barbara, USA

Louis M. PecoraUS Naval Research Laboratory, USA

Anthony RobertsUniversity of Adelaide, Australia

Björn SandstedeBrown University, USA

Mary SilberNorthwestern University, USA

Michael J. WardUniversity of British Columbia, Canada

SIAM Registration Desk The SIAM registration desk is located in the Ballroom Foyer. It is open during the following times:

Saturday, May 16

8:00 AM - 8:00 PM

Sunday, May 17

8:00 AM - 5:00 PM

Monday, May 18

8:00 AM - 6:30 PM

Tuesday, May 19

8:00 AM - 4:30 PM

Wednesday, May 20

8:00 AM - 4:30 PM

Thursday, May 21

8:00 AM - 4:45 PM

Hotel Address Snowbird Ski and Summer Resort 9320 S. Cliff Lodge Drive Snowbird, UT 84092-9000 USA

Hotel web address: http://www.snowbird.com/

Hotel Telephone NumberTo reach an attendee or leave a message, call +1-801-742-2222. If the attendee is a hotel guest, the hotel operator can connect you with the attendee’s room.

Hotel Check-in and Check-out TimesCheck-in time is 4:00 PM and check-out time is 11:00 AM.

Child CareAs a service to SIAM attendees, SIAM has made arrangements for in-room child care. All sitters should be requested with at least 48 hours notice. If you have not already made reservations for child care and would like to inquire about availability, please contact Camp Snowbird at (801)933-2256, or e-mail the camp at [email protected].

Corporate Members and AffiliatesSIAM corporate members provide their employees with knowledge about, access to, and contacts in the applied mathematics and computational sciences community through their membership benefits. Corporate membership is more than just a bundle of tangible products and services; it is an expression of support for SIAM and its programs. SIAM is pleased to acknowledge its corporate members and sponsors. In recognition of their support, non-member attendees who are employed by the following organizations are entitled to the SIAM member registration rate.

Corporate Institutional MembersThe Aerospace Corporation

Air Force Office of Scientific Research

Aramco Services Company

AT&T Laboratories - Research

Bechtel Marine Propulsion Laboratory

The Boeing Company

CEA/DAM

Department of National Defence (DND/CSEC)

DSTO- Defence Science and Technology Organisation

ExxonMobil Upstream Research

Hewlett-Packard

IBM Corporation

IDA Center for Communications Research, La Jolla

IDA Center for Communications Research, Princeton

Institute for Computational and Experimental Research in Mathematics (ICERM)

Institute for Defense Analyses, Center for Computing Sciences

Lawrence Berkeley National Laboratory

2015 SIAM Conference on Applications of Dynamical Systems 3

Lockheed Martin

Los Alamos National Laboratory

Mathematical Sciences Research Institute

Max-Planck-Institute for Dynamics of Complex Technical Systems

Mentor Graphics

National Institute of Standards and Technology (NIST)

National Security Agency (DIRNSA)

Oak Ridge National Laboratory, managed by UT-Battelle for the Department of Energy

Sandia National Laboratories

Schlumberger-Doll Research

Tech X Corporation

U.S. Army Corps of Engineers, Engineer Research and Development Center

United States Department of Energy

List current March 2015.

Funding AgenciesSIAM and the Conference Organizing Committee wish to extend their thanks and appreciation to the U.S. National Science Foundation and the U.S. Department of Energy for their support of this conference.

Leading the applied mathematics community …Join SIAM and save!

SIAM members save up to $130 on full registration for the 2015 SIAM Conference on Dynamical Systems (DS15)! Join your peers in supporting the premier professional society for applied mathematicians and computational scientists. SIAM members receive subscriptions to SIAM Review, SIAM News and SIAM Unwrapped, and enjoy substantial discounts on SIAM books, journal subscriptions, and conference registrations.

If you are not a SIAM member and paid the Non-Member or Non-Member Mini Speaker/Organizer rate to attend the conference, you can apply the difference between what you paid and what a member would have paid ($130 for a Non-Member and $65 for a Non-Member Mini Speaker/Organizer) towards a SIAM membership. Contact SIAM Customer Service for details or join at the conference registration desk.

If you are a SIAM member, it only costs $10 to join the SIAM Activity Group on Dynamical Systems (SIAG/DS). As a SIAG/DS member, you are eligible for an additional $10 discount on this conference, so if you paid the SIAM member rate to attend the conference, you might be eligible for a free SIAG/DS membership. Check at the registration desk.

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Join onsite at the registration desk, go to www.siam.org/joinsiam to join online or download an application form, or contact SIAM Customer Service:

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Standard Audio/Visual Set-Up in Meeting Rooms SIAM does not provide computers for any speaker. When giving an electronic presentation, speakers must provide their own computers. SIAM is not responsible for the safety and security of speakers’ computers.

The Plenary Session Room will have two (2) screens, one (1) data projector and one (1) overhead projector. The data projectors support VGA connections only. Presenters requiring an HDMI or alternate connection must provide their own adaptor.

All other concurrent/breakout rooms will have one (1) screen and one (1) data projector. The data projectors support VGA connections only. Presenters requiring an HDMI or alternate connection must provide their own adaptor.

If you have questions regarding availability of equipment in the meeting room of your presentation, please see a SIAM staff member at the registration desk.

Internet AccessComplimentary wireless Internet access will be available in the guest rooms and public areas of the Cliff Lodge, the Lodge at Snowbird, and the Inn. Additionally, complimentary wireless Internet access will be available in the meeting space of the Cliff Lodge.

Email stations will also be available during registration hours.

Registration Fee Includes• Admission to all technical sessions

• Business Meeting (open to SIAG/DS members)

• Coffee breaks daily

• Poster Sessions and Dessert Receptions

• Room set-ups and audio/visual equipment

• Welcome Reception


Job PostingsPlease check with the SIAM registration desk regarding the availability of job postings or visit http://jobs.siam.org.

Important Notice to Poster PresentersPoster Session 1 is scheduled for Tuesday, May 19, 8:30 PM-10:30 PM. Poster Session 1 presenters are requested to put up their posters in the Ballroom between 8:00 and 8:30 PM on Tuesday, at which time boards and push pins will be available. Poster displays must be removed at 10:30 PM, the end of Poster Session 1. Posters remaining after this time will be discarded. SIAM is not responsible for discarded posters.

Poster Session 2 is scheduled for Wednesday, May 20, 8:30 PM-10:30 PM. Poster Session 2 presenters are requested to put up their posters in the Ballroom between 8:00 and 8:30 PM on Wednesday, at which time boards and push pins will be available. Poster displays must be removed at 10:30 PM, the end of Poster Session 2. Posters remaining after this time will be discarded. SIAM is not responsible for discarded posters.

For information about preparing a poster, please visit http://www.siam.org/meetings/guidelines/presenters.php.

SIAM Books and JournalsDisplay copies of books and complimentary copies of journals are available on site. SIAM books are available at a discounted price during the conference. If a SIAM books representative is not available, completed order forms and payment (credit cards are preferred) may be taken to the SIAM registration desk. The books table will close at 11:00 AM on Thursday, May 21.

Journal Editor Panel SponsorsAIP Publishing (Chaos)

APS Publishing (PRL and PRE)

Elsevier Publishing (Physica D)

Elsevier Publishing (Physics Letters A)

IOP Publishing (Nonlinearity)

Table Top DisplaysAIP Publishing

Elsevier

IOP Publishing

Oxford University Press

SIAM

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Cynthia Phillips, SIAM Vice President for Programs ([email protected]).

Please NoteSIAM is not responsible for the safety and security of attendees’ computers. Do not leave your laptop computers unattended. Please remember to turn off your cell phones, pagers, etc. during sessions.

Get-togethers • Welcome Reception

Saturday, May 16

6:00 PM – 8:00 PM

• Business Meeting (open to SIAG/DS members)

Monday, May 18

8:30 PM - 9:30 PM

Complimentary beer and wine will be served.

• Poster Session and Dessert Reception I

Tuesday, May 19 8:30 PM - 10:30 PM

• Poster Session and Dessert Reception II

Wednesday, May 20 8:30 PM - 10:30 PM

Recording of PresentationsAudio and video recording of presentations at SIAM meetings is prohibited without the written permission of the presenter and SIAM.

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Featured MinisymposiaFeatured Minisymposia will include a selective group of talks that describe and promote recent significant advances in

a theme deemed to be of high priority for current and near future research in Dynamical Systems and their Applications.

Sunday, May 17

2:00 PM – 4:00 PM

MS14: Applications of Algebraic Topology to NeuroscienceRoom: Ballroom I

Organizers:Chad Giusti, University of Pennsylvania, USA

Robert W. Ghrist, University of Pennsylvania, USADanielle Bassett, University of Pennsylvania, USA

MS15: Data Assimilation in the Life SciencesRoom: Ballroom II

Organizers:Elizabeth M. Cherry, Cornell University, USA

Timothy Sauer, George Mason University, USA

MS16: Data-Driven Modeling of Dynamical Processes in Spatially-Embedded Random Networks

Room: MaybirdOrganizer: Gyorgy Korniss, Rensselaer Polytechnic Institute, USA

MS17: Stochastic Delayed NetworksRoom: Primrose A

Organizer: Gabor Orosz, University of Michigan, Ann Arbor, USA

MS18: Localized Pattern Formation in Reaction-diffusion EquationsRoom: Primrose B

Organizer: Arik Yochelis, Ben Gurion University Negev, Israel


Featured Minisymposia

Wednesday, May 20

4:00 PM - 6:00 PM

MS104: Non-Autonomous InstabilitiesRoom: Ballroom I

Organizer: Sebastian M. Wieczorek, University College Cork, Ireland

MS105: Random Walks, First Passage Time and ApplicationsRoom: Ballroom II

Organizers:Theodore Kolokolnikov, Dalhousie University, Canada

Sidney Redner, Santa Fe Institute, USA

MS106: Time-Delayed FeedbackRoom: Wasatch B

Organizer: Andreas Amann, University College Cork, Ireland

MS107: Emerging Strategies for Stability Analysis of Electrical Power GridsRoom: Maybird

Organizers:Lewis G. Roberts, University of Bristol, United Kingdom

Florian Dorfler, ETH Zürich, Switzerland

MS108: Invariant Manifolds Unravelling Complicated DynamicsRoom: Primrose A

Organizers:Stefanie Hittmeyer, University of Auckland, New Zealand

Pablo Aguirre, Universidad Técnica Federico Santa María, Chile

MS109: Medical ApplicationsRoom: Primrose B

Organizers:Dan D. Wilson, University of California, Santa Barbara, USAJeff Moehlis, University of California, Santa Barbara, USA


Minitutorials

Sunday, May 17

2:00 PM - 4:00 PMMT1: Network Dynamics

Room: Ballroom IIIOrganizer: Louis M. Pecora, United States Naval Research Laboratory, USA

Wednesday, May 20

4:00 PM - 6:00 PMMT2: Stochastic Dynamics of Rare Events

Room: Ballroom IIIOrganizer: Eric Forgoston, Montclair State University, USA


Sunday, May 17

11:45 AM - 12:30 PM IP1 Advances on the Control of Nonlinear Network Dynamics

Adilson E. Motter, Northwestern University, USA

Monday, May 18

11:00 AM - 11:45 AM IP2 Mathematics of Crime

Andrea L. Bertozzi, University of California, Los Angeles, USA

6:00 PM - 6:45 PM IP3 Filtering Partially Observed Chaotic Deterministic Dynamical Systems

Andrew Stuart, University of Warwick, United Kingdom

Tuesday, May 19

11:00 AM - 11:45 AM IP4 Fields of Dreams: Modeling and Analysis of Large Scale Activity in the Brain

Bard Ermentrout, University of Pittsburgh, USA

Invited Plenary Speakers

** All Invited Plenary Presentations will take place in the Ballroom**


Invited Plenary Speakers

Wednesday, May 20

11:00 AM - 11:45 AM

IP5 Cooperation, Cheating, and Collapse in Biological Populations

Jeff Gore, Massachusetts Institute of Technology, USA

Thursday, May 21

11:15 AM - 12:00 PM

IP6 Brain Control - It’s Not Just for Mad Scientists

Jeff Moehlis, University of California, Santa Barbara, USA

4:15 PM - 5:00 PM

IP7 The Robotic Scientist: Distilling Natural Laws from Raw Data, from Robotics to Biology and Physics

Hod Lipson, Cornell University, USA


Prize Presentation and Special Lecture**The Prize Presentation and Special Lecture will take place in the Ballroom.**

SIAM Activity Group on Dynamical Systems Prizes

Sunday, May 17

8:00 PM - 8:15 PM

Prize Presentations - Jürgen Moser and J. D. Crawford

J. D. Crawford Prize Recipient

Florin Diacu, University of Victoria, Canada

Jürgen Moser Lecturer

John Guckenheimer, Cornell University, USA

8:15 PM - 9:00 PM

Jürgen Moser Lecture: Dynamics and Data



SIAM Activity Group on Dynamical Systems (SIAG/DS)www.siam.org/activity/ds

A GREAT WAY TO GET INVOLVED! Collaborate and interact with mathematicians and applied scientists whose work involves dynamical systems.

ACTIVITIES INCLUDE: • DSWeb portal► • Special sessions at SIAM meetings► • Biennial conference► • Jürgen Moser Lecture► • J. D. Crawford Prize► • Red Sock Award

BENEFITS OF SIAG/DS MEMBERSHIP: • Listing in the SIAG’s online membership directory • Additional $10 discount on registration at the SIAM Conference on Applied Dynamical Systems (excludes students)

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2015

2014-15 SIAG/DS OFFICERS Chair: Timothy D Sauer, George Mason University Vice Chair: Vivi Rottschafer, Universiteit Leiden Program Director: Lora Billings, Montclair State University Secretary and DS Magazine Chief Editor: Elizabeth Cherry, Rochester Institute of Technology DSWeb Portal Editor-in-Chief: Peter van Heijster, Queensland University of Technology


Final Program

2015


Saturday, May 16

Registration8:00 AM-8:00 PMRoom:Ballroom Foyer

SIAM Workshop on Network Science (May 16-17 -- separate fees apply)9:00 AM-8:30 PMRoom:Cottonwood Room - Snowbird Center

Welcome Reception6:00 PM-8:00 PMRoom:Ballroom

Sunday, May 17Registration8:00 AM-5:00 PMRoom:Ballroom Foyer

SIAM Workshop on Network Science (May 16-17 -- separate fees apply)8:30 AM-6:00 PMRoom:Cottonwood Room - Snowbird Center

Sunday, May 17

MS1Patterns in Partial Differential Equations - Part I of II9:00 AM-11:00 AMRoom:Ballroom I

For Part 2 see MS19 Patterns play an important role in the dynamics of many dissipative and dispersive PDEs, posed on large or unbounded domains. This minisymposium will feature contributions that investigate intrinsically multi-dimensional aspects of the dynamics of patterns, including their existence, stability, instability, slow evolution, and interaction. Examples include interfaces between patterned and un-patterned state, point defects or vortices, and line defects. We expect to bring together researchers with a variety of backgrounds, employing a variety of techniques, such as diffusive and dispersive stability estimates, energy methods from the calculus of variations, or spatial dynamics and bifurcation methods.

Organizer: Keith PromislowMichigan State University, USA

Organizer: Noa KraitzmanMichigan State University, USA

9:00-9:25 Bifurcation and Competitive Evolution of Network Morphologies in the Strong Functionalized Cahn-Hilliard EquationNoa Kraitzman, Michigan State University,

USA

9:30-9:55 Nonlinearity Saturation as a Singular Perturbation of the Nonlinear Schrödinger EquationKarl Glasner, University of Arizona, USA

10:00-10:25 Dark-Bright, Dark-Dark, Vortex-Bright and Other Multi-Component NLS Beasts: Theory and Recent ApplicationsPanayotis Kevrekidis, University of

Massachusetts, USA

10:30-10:55 Nonlinear Stability of Source DefectsBjorn Sandstede, Brown University, USA


Sunday, May 17

MS2Dynamics of Boolean Switching Networks9:00 AM-11:00 AMRoom:Ballroom II

Modeling complex systems in general, and gene regulation in particular, presents particular challenges. The challenges include the large size of biologically relevant gene networks and the ability to parameterize ODE models. The available data are often only qualitative and therefore it is not clear how to compare them to a precise solutions of an ODE system. An attractive answer to these challenges is the framework of switching systems, which combine continuous time evolution of an ODE system with discrete, or Boolean quantization of the phase space. The minisymposium will bring together the leading researchers in the area to provide an overview of this very active field.

Organizer: Tomas GedeonMontana State University, USA

Organizer: Roderick EdwardsUniversity of Victoria, Canada

9:00-9:25 Database for Switching Networks As a Tool for Study of Gene NetworksTomas Gedeon, Montana State University,

USA

9:30-9:55 Gene Network Models Including mRNA and Protein DynamicsRoderick Edwards, University of Victoria,

Canada

10:00-10:25 Evolution of Gene NetworksLeon Glass, McGill University, Canada

10:30-10:55 Dynamics of Autonomous Boolean NetworksOtti D’Huys and Nicholas D. Haynes,

Duke University, USA; Miguel C. Soriano and Ingo Fischer, Universitat de les Illes Balears, Spain; Daniel J. Gauthier, Duke University, USA

Sunday, May 17

MS3Ocean-in-the-loop: Towards Real-Time Monitoring in Geophysical Flows - Part I of II9:00 AM-11:00 AMRoom:Ballroom III

For Part 2 see MS21 Improved modeling and prediction of fluid dynamics is needed to better understand ocean and atmospheric transport along with associated applications including contaminant dispersion, environmental modeling, and underwater acoustic propagation. Major recent advances in closed-loop adaptive sampling, Lagrangian data assimilation, uncertainty quantification, and phase space transport are providing improved understanding of transport phenomena. The purpose of this minisymposium is to expose the audience to recent progress and developments, as well as to bring together researchers developing new mathematical methods and applications for use in understanding flow transport.

Organizer: Eric ForgostonMontclair State University, USA

Organizer: Ani HsiehDrexel University, USA

9:00-9:25 Tracking of Geophysical Flows by Robot Teams: An Experimental ApproachAni Hsieh, Dhanushka Kularatne, and

Dennis Larkin, Drexel University, USA; Eric Forgoston, Montclair State University, USA; Philip Yecko, Cooper Union, USA

9:30-9:55 Controlled Lagrangian Prediction Using An Ensemble of Flow ModelsFumin Zhang, Georgia Institute of

Technology, USA

10:00-10:25 Conditional Statistics with Lagrangian Coherent StructuresWenbo Tang and Phillip Walker, Arizona

State University, USA

10:30-10:55 Controlling Long-Term Spatial Distributions of Autonomous Vehicles in Stochastic Flow EnvironmentsChristoffer R. Heckman, University of

Colorado Boulder, USA; Ani Hsieh, Drexel University, USA; Ira B. Schwartz, Naval Research Laboratory, USA

Sunday, May 17

MS4Dynamics of Rigid Bodies and Fluids9:00 AM-11:00 AMRoom:Magpie A

This interdisciplinary minisymposium will address mathematical methods used in the rigid body mechanics, fluid mechanics, and fluid-structure interaction. The lectures will include topics on dynamics of nonholonomic systems, coupled rigid body and fluid motion, links between nonholonomic mechanics and fluids, and a geometric approach to numerical fluid dynamics. The unifying idea of this minisymposium is the representation of the rigid body and fluid dynamics in the form of of the Euler-Poincare (resp., Lie-Poisson) equations in the Lagrangian (resp., Hamiltonian) setting.

Organizer: Dmitry ZenkovNorth Carolina State University, USA

Organizer: Scott D. KellyUniversity of Illinois at Urbana-Champaign, USA

9:00-9:25 The Lie-Dirac Reduction for Nonholonomic Systems on Semidirect ProductsHiroaki Yoshimura, Waseda University,

Japan; François Gay-Balmaz, Ecole Normale Superieure de Paris, France

9:30-9:55 Discretization of Hamiltonian Incompressible FluidsGemma Mason, California Institute of

Technology, USA; Christian Lessig, Technische Universität Berlin, Germany; Mathieu Desbrun, California Institute of Technology, USA

10:00-10:25 Constrained Motion of Point Vortices Interacting Dynamically with Rigid Bodies in Ideal FlowMichael Fairchild and Scott Kelly,

University of North Carolina, Charlotte, USA

10:30-10:55 The Poincare-Hopf Theorem in Nonholonomic MechanicsOscar Fernandez, Wellesley College,

USA; Anthony M. Bloch, University of Michigan, USA; Dmitry Zenkov, North Carolina State University, USA


Sunday, May 17

MS9Dynamics on Networks and Network Topology in Ecology and Epidemiology9:00 AM-11:00 AMRoom:Superior A

The spread of pathogens in population networks or of invasive species in fragmented landscapes give rise to dynamical systems defined on networks. The topology of the network has implications for the dynamics, constraining, for example, if spread through the network is wave-like or if new clusters can form at long distances from old ones. New topological tools such as persistent topology developed for studying data sets such as large point clouds or networks allow for new insights into dynamics on networks. Topics in the minisymposium include spatially embedded contagion networks and network-mediated dynamical systems models in ecology and epidemiology, all informed by the underlying network topology.

Organizer: Christopher StricklandUniversity of North Carolina at Chapel Hill, USA

Organizer: Patrick ShipmanColorado State University, USA

9:00-9:25 Network Spread and Control of Invasive Species and Infectious DiseasesChristopher Strickland, University of

North Carolina at Chapel Hill, USA; Patrick Shipman, Colorado State University, USA

9:30-9:55 Topological Data Analysis for and with Contagions on NetworksDane Taylor, University of North Carolina

at Chapel Hill, USA; Florian Klimm, Humboldt University Berlin, Germany; Heather Harrington, University of Oxford, United Kingdom; Miroslav Kramar and Konstantin Mischaikow, Rutgers University, USA; Mason A. Porter, University of Oxford, United Kingdom; Peter J. Mucha, University of North Carolina at Chapel Hill, USA

Sunday, May 17

MS7The Dynamics and Computation of Neuronal Networks9:00 AM-11:00 AMRoom:Wasatch B

The dynamics of neuronal networks provide rich information regarding the nature of computation and information encoding in the brain. This minisymposium explores recent work in the modeling of neuronal dynamics, emphasizing implications on sensory processing and network connectivity. The speakers will draw particular attention to new mathematical advances in characterizing the structure-function relationship for complex neuronal networks and techniques for understanding the biophysical processes underlying network dynamics.

Organizer: Victor BarrancaNew York University, USA

Organizer: Douglas ZhouShanghai Jiao Tong University, China

9:00-9:25 Reconstruction of Structural Connectivity in Neuronal Networks Using Compressive Sensing of Network DynamicsVictor Barranca, New York University,

USA; Douglas Zhou, Shanghai Jiao Tong University, China; David Cai, Shanghai Jiao Tong University, China and Courant Institute of Mathematical Sciences, New York University, USA

9:30-9:55 Theoretical Modeling of Neuronal Dendritic IntegrationSongting Li, Courant Institute of

Mathematical Sciences, New York University, USA; Douglas Zhou, Shanghai Jiao Tong University, China; David Cai, Courant Institute of Mathematical Sciences, New York University, USA

10:00-10:25 Topology Reconstruction of Neuronal NetworksDouglas Zhou, Yanyang Xiao, Yaoyu

Zhang, and Zhiqin Xu, Shanghai Jiao Tong University, China; David Cai, Shanghai Jiao Tong University, China and Courant Institute of Mathematical Sciences, New York University, USA

10:30-10:55 Functional Connectomics from Data: Constructing Probabilistic Graphical Models for Neuronal NetworksEli Shlizeman, University of Washington,

USA

Sunday, May 17

MS8Wave-turbulence Interactions in Geophysical and Astrophysical Fluid Dynamics9:00 AM-11:00 AMRoom:Maybird

The interaction of waves and turbulence is a topic of fundamental importance in geophysical and astrophysical fluid dynamics, where wave dynamics result from density stratification, rotation, magnetism, and compressibility. The interactions of wave dynamics with turbulence can have significant implications, transferring energy over long distances or across scales, and impacting the formation and evolution of coherent structures. This minisymposium brings together researchers to present recent results in wave-turbulence interaction in both geophysical and astrophysical settings.

Organizer: Ian GroomsNew York University, USA

Organizer: Jared P. WhiteheadBrigham Young University, USA

9:00-9:25 Internal Wave Generation by ConvectionDaniel Lecoanet, University of California,

Berkeley, USA; Keaton Burns, Massachusetts Institute of Technology, USA; Geoffrey M. Vasil, University of Sydney, Australia; Eliot Quataert, University of California, Berkeley, USA; Benjamin Brown, University of Colorado Boulder, USA; Jeffrey Oishi, Farmingdale State College, USA

9:30-9:55 Interaction of Inertial Oscillations with a Geostrophic FlowJim Thomas, Courant Institute of

Mathematical Sciences, New York University, USA; Shafer Smith, Courant Institute, Center for Atmosphere Ocean Science, USA; Oliver Buhler, Courant Institute of Mathematical Sciences, New York University, USA

10:00-10:25 Investigation of Boussinesq non-linear Interactions Using Intermediate ModelsGerardo Hernandez-Duenas, National

University of Mexico, Mexico; Leslie Smith, University of Wisconsin, USA; Samuel Stechmann, University of Wisconsin, Madison, USA

10:30-10:55 Interactions Between Near-Inertial Waves and Turbulence in the OceanJacques Vanneste, University of Edinburgh,

United Kingdom

continued on next page


10:00-10:25 Local Inference of Gene Regulatory Networks from Time Series DataFrancis C. Motta, Kevin McGoff, Anastasia

Deckard, Xin Guo Guo, Tina Kelliher, Adam Leman, Steve Haase, and John Harer, Duke University, USA

10:30-10:55 Patterns in Discrete Ecological Dynamical Systems Revealed Through Persistent HomologyRachel Neville, Colorado State University,

USA

Sunday, May 17

MS10Dynamics Modeling with Transformations Between Partial- and Delay Differential Equations9:00 AM-11:00 AMRoom:Superior B

Travelling wave solutions of the governing partial differential equations (PDEs) of distributed parameter systems often lead to the transformation of the infinite dimensional problem to a corresponding system of delay differential equations (DDEs). The transformations from DDEs to PDEs may also be useful for analyzing certain classes of dynamical systems. The lectures give a spectrum of these transformations revealing the intricate dynamical properties of these systems, like the peculiar stability properties of periodic retarded systems, neutral systems with multiple delays, tau-nonstabilizable systems, delayed boundary value problems and variable delay systems, which are often linked to models of dynamic contact problems.

Organizer: Gabor StepanBudapest University of Technology and Economics, Hungary

9:00-9:25 What Is Wrong with Non-Smooth Mechanics and How Memory Effects Can Fix It?Robert Szalai, University of Bristol, United

Kingdom

9:30-9:55 Differential Equations with Variable Delay and Their Connection to Partial Differential EquationsGunter Radons, Andreas Otto, and

David Mueller, Chemnitz University of Technology, Germany

10:00-10:25 Stability Analysis of PDEs with Two Spatial Dimensions Using Lyapunov Methods and SOSEvgeny Meyer and Matthew Peet, Arizona


10:30-10:55 Delayed Boundary Conditions in Control of ContinuaGabor Stepan, Budapest University of

Technology and Economics, Hungary; Li Zhang, Nanjing University of Aeronautics and Astronautics, China

Sunday, May 17

MS11Multiscale Models to Understand the Social and Physical World - Part I of II9:00 AM-11:00 AMRoom:White Pine

For Part 2 see MS29 The scientific community has developed a rich and diverse library of mathematical models capable of capturing complex processes and interactions over a broad range of scales in space and time. In this session, we feature a variety of researchers exploring the application of mathematical models to the social and physical world. The topics of this session cover several scales, from interacting particles to population models to PDEs, and include both stochastic and deterministic models. Talks will address applications such as earthquakes, swimming microorganisms, and human crowd dynamics.

Organizer: Alethea BarbaroCase Western Reserve University, USA

Organizer: Brittany EricksonPortland State University, USA

9:00-9:25 Phase Transitions in Models for Social DynamicsAlethea Barbaro, Case Western Reserve

University, USA

9:30-9:55 A Center Manifold and Complex Phases for a Large Number of Interacting ParticlesBjorn Birnir, University of California, Santa

Barbara, USA; Luis Bonilla, Universidad Carlos III de Madrid, Spain; Jorge Cornejo-Donoso, University of California, Santa Barbara, USA

10:00-10:25 Mathematical Challenges in Ground State Formation of Isotropic and Anisotropic InteractionDavid T. Uminsky, University of San

Francisco, USA

10:30-10:55 Modeling Earthquake Cycles on Faults Separating Variable MaterialsBrittany Erickson, Portland State University,

USA


Sunday, May 17

MS12Network Synchronization in Mechanical Systems and Beyond - Part I of II9:00 AM-11:00 AMRoom:Primrose A

For Part 2 see MS30 This minisymposium focuses on the role of synchronization, coordination, and dynamical consensus in mechanical systems and beyond. Examples range from bridges and mechanical pendula to self-organizing networks of moving agents, with application in robotics and animal behavior. This minisymposium aims at various theoretical and experimental aspects of synchrony-induced phenomena and their control and brings together applied mathematicians and mechanical engineers.

Organizer: Igor BelykhGeorgia State University, USA

Organizer: Maurizio PorfiriPolytechnic Institute of New York University, USA

9:00-9:25 Wind-Induced Synchrony Causes the Instability of a Bridge: When Millennium Meets TacomaIgor Belykh and Russell Jeter, Georgia

State University, USA; Vladimir Belykh, Lobachevsky State University of Nizhny Novgorod, Russia

9:30-9:55 Versatile Vibrations: Partially Synchronized States in Mechanical Systems from Microns to KilometersDaniel Abrams, Northwestern University,

USA

10:00-10:25 Synchronization over Networks Inspired by Echolocating BatsSubhradeep Roy and Nicole Abaid, Virginia

Tech, USA

10:30-10:55 Network Graph Can Promote Faster Consensus Reach Despite Large Inter-Agent DelaysMin Hyong Koh and Rifat Sipahi,

Northeastern University, USA

Sunday, May 17

MS23Oscillations in Systems with Relays9:00 AM-11:00 AMRoom:Magpie B

This minisymposium aims to strengthen the link between the theory and applications of systems with relay nonlinearities. A particular attention will be given to those theoretical tools that allow designing closed orbits in real life applications. Both local bifurcation technique and available global methods will be addressed. On the modelling side, the minisymposium covers the relay systems described by discontinuous differential equations as well as functional-differential equations with hysteresis operators.

Organizer: Dmitry RachinskiyUniversity of Texas at Dallas, USA

9:00-9:25 Population Dynamics with the Preisach OperatorDmitry Rachinskiy, University of Texas at

Dallas, USA

9:30-9:55 Self-Oscillations Via Two-Relay Controller: Design, Analysis, and ApplicationsLuis T. Aguilar, Instituto Politécnico

Nacional, Mexico; Igor Boiko, The Petroleum Institute of Abu Dhabi, United Arab Emirates; Leonid Fridman and Rafael Iriarte, Universidad Nacional Autonoma de Mexico, Mexico

10:00-10:25 Periodic Solutions in Dynamical Systems with Relay: Existence, Stability, BifurcationsPavel Gurevich, Free University of Berlin,

Germany

10:30-10:55 Reaction-Diffusion Equations with Discontinuous Relay NonlinearitySergey Tikhomirov, St. Petersburg State

University, Russia; Pavel Gurevich, Free University of Berlin, Germany

Sunday, May 17

MS13Dynamics of High Dimensional Stochastic Models9:00 AM-11:00 AMRoom:Primrose B

High dimensional models can arise from spatially extended systems or systems with large numbers of interacting units (i.e. atoms, neurons, people, ect.). The observed global behavior of these systems can be characterized through the analysis and simulation of large dimensional differential equation (SDE) and stochastic partial differential equation (SPDE) models. We look at applications including pattern formation, ferromagnets, molecular dynamics, and viscoelastic fluids.

Organizer: Katherine NewhallUniversity of North Carolina at Chapel Hill, USA

9:00-9:25 Low-Damping Transition Times in a Ferromagnetic Model SystemKatherine Newhall, University of North

Carolina at Chapel Hill, USA

9:30-9:55 Tipping and Warning Signs for Patterns and Propagation Failure in SPDEsChristian Kuehn, Vienna University of

Technology, Austria; Karna V. Gowda, Northwestern University, USA

10:00-10:25 Fluctuating Hydrodynamics of Microparticles in Viscoelastic FluidsScott McKinley, University of Florida, USA

10:30-10:55 Stochastic Boundary Conditions for Molecular Dynamics: From Crystal to MeltGregory J. Herschlag, Duke University,

USA; Sorin Mitran, University of North Carolina, Chapel Hill, USA


Sunday, May 17

MS116Torus Canards in Applications9:00 AM-11:00 AMRoom:Wasatch A

Torus canards arise in slow/fast systems in which the fast subsystem contains families of attracting and repelling limit cycles that meet in a saddle-node bifurcation of limit cycles. In models of neuronal systems, the transition from spiking (rapid firing of the membrane potential) to bursting (alternating intervals of spiking and quiescence) can occur via torus canards. Characterised by long excursions near the repelling manifold of limit cycles, torus canards are the higher-dimensional analogue of classical canards. This minisymposium consists of case studies that illustrate how torus canards give rise to rich dynamical phenomena in various applications.

Organizer: Kerry-Lyn RobertsUniversity of Sydney, Australia

Organizer: Theodore VoBoston University, USA

9:00-9:25 The Interaction Between Classical Canards and Torus CanardsTheodore Vo, Boston University, USA

9:30-9:55 Averaging and Generic Torus CanardsKerry-Lyn Roberts, University of Sydney,

Australia

10:00-10:25 Averaging and Kam Theory in Torus CanardsAlbert Granados, INRIA, France

10:30-10:55 Torus Canard BreakdownAndrey Shilnikov, Georgia State University,

USA; Alexander Neiman, Ohio University, USA

Sunday, May 17Coffee Break11:00 AM-11:30 AMRoom:Golden Cliff

Welcome Remarks11:30 AM-11:45 AMRoom:Ballroom

Sunday, May 17

IP1Advances on the Control of Nonlinear Network Dynamics11:45 AM-12:30 PMRoom:Ballroom

Chair: Louis M. Pecora, Naval Research Laboratory, USA

An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control. In this talk, I will discuss recent advances on mathematical and computational approaches to control high-dimensional nonlinear network dynamics under general constraints on the admissible interventions. I will present applications to the stabilization of power grids, identification of new therapeutic targets, mitigation of extinctions in food webs, and control of systemic failures in socio-economic systems. These examples will illustrate the potential and limitations of existing methods to address a broad class of problems, ranging from cascade control and transient stability to network reprogramming in general.

Adilson E. MotterNorthwestern University, USA

Lunch Break12:30 PM-2:00 PMAttendees on their own


Sunday, May 17

MT1Network Dynamics2:00 PM-4:00 PMRoom:Ballroom III

Chair: Louis M. Pecora, Naval Research Laboratory, USA

Over the last decade or more analysis of networks has developed into a topic all its own in mathematics and many sciences (physics, biology, sociology, neuroscience, etc.). Many journals have sections for papers on network analysis. This minitutorial will present the audience with an overview of network science including useful techniques and tools along with more abstract concepts. The speakers will also comment on new ideas and approaches that are beginning to surface.

From Structure to Dynamics in Complex NetworksMichelle Girvan, University of Maryland,

USA

Networks, Dynamics, and the Ongoing EvolutionMason A. Porter, University of Oxford,

United Kingdom

Sunday, May 17

MS15Featured Minisymposium: Data Assimilation in the Life Sciences2:00 PM-4:00 PMRoom:Ballroom II

Assimilation of data with models of physical and biological processes is a crucial component of modern scientific analysis. In recent years, nonlinear versions of Kalman filtering have been developed, in addition to methods that estimate model parameters in parallel with the system state. This minisymposium highlights the state of the art in applying these techniques to nonlinear dynamical systems in the life sciences to gain understanding from biological data. The talks will illustrate the use of data assimilation to analyze the dynamics of several prototypical systems, such as cardiac tissue, hippocampal neurons and neural cultures.

Organizer: Elizabeth M. CherryCornell University, USA

Organizer: Timothy SauerGeorge Mason University, USA

2:00-2:25 Intramural Forecasting of Cardiac Dynamics Using Data AssimilationMatthew J. Hoffman, Rochester Institute

of Technology, USA; Elizabeth M. Cherry, Cornell University, USA

2:30-2:55 Reconstructing Dynamics of Unmodeled VariablesFranz Hamilton and Timothy Sauer,

George Mason University, USA

3:00-3:25 Modeling Excitable Dynamics of Cardiac CellsSebastian Berg, T.K. Shajahan, Jan

Schumann-Bischoff, Ulrich Parlitz, and Stefan Luther, Max Planck Institute for Dynamics and Self-Organization, Germany

3:30-3:55 Tracking Neuronal Dynamics During Seizures and Alzheimer’s DiseaseGhanim Ullah, University of South Florida,

USA

Sunday, May 17

MS14Featured Minisymposium: Applications of Algebraic Topology to Neuroscience2:00 PM-4:00 PMRoom:Ballroom I

The varied subjects of study in neuroscience, from brain network dynamics to clinical diagnosis, provide an abundant source of fundamentally non-linear problems which emerging tools in computational algebraic topology are well-suited to address. Conversely, these new applications call for the development of new theoretical structure through which to interpret results and form hypotheses. This minisymposium showcases some recent applications and the directions in which the theory is evolving to accommodate them.

Organizer: Chad GiustiUniversity of Pennsylvania, USA

Organizer: Robert W. GhristUniversity of Pennsylvania, USA

Organizer: Danielle BassettUniversity of Pennsylvania, USA

2:00-2:25 Topological Detection of Structure in Neural Activity RecordingsChad Giusti, University of Pennsylvania,

USA; Carina Curto and Vladimir Itskov, Pennsylvania State University, USA

2:30-2:55 An Algebro-Topological Perspective on Hierarchical Modularity of NetworksKathryn Hess, École Polytechnique

Fédérale de Lausanne, Switzerland

3:00-3:25 The Topology of Fragile X SyndromeDavid Romano, Stanford University School

of Medicine, USA

3:30-3:55 The Neural Ring: Using Algebraic Geometry to Analyze Neural CodesNora Youngs, Harvey Mudd College, USA


Sunday, May 17

MS16Featured Minisymposium: Data-Driven Modeling of Dynamical Processes in Spatially-Embedded Random Networks2:00 PM-4:00 PMRoom:Maybird

Infrastructure, transportation, and brain networks are embedded in strongly heterogeneous spatial environments, posing formidable challenges in understanding the vulnerability or “plasticity” of these systems. There exists a large gap between some universal features of simplified dynamical processes on non-spatial complex networks and their applicability to real-world problems. This minisymposium will present recent progress by data-driven approaches in diverse areas. Topics will include the lack of self-averaging and predictability of cascading failures in power grids, optimization in smart grids, the applicability of scaling laws of human travel, and the impact of wiring constraints and weight-based heterogeneity in the cortical networks.

Organizer: Gyorgy KornissRensselaer Polytechnic Institute, USA

2:00-2:25 Cascading Failures and Stochastic Methods for Mitigation in Spatially-Embedded Random NetworksGyorgy Korniss, Rensselaer Polytechnic

Institute, USA

2:30-2:55 Feasibility of Micro-Grid Adoptions in Spatially-Embedded Urban NetworksMarta Gonzalez, Massachusetts Institute of

Technology, USA

3:00-3:25 Spatial Distribution of Population and Scaling in Human TravelZoltan Neda, Babes-Bolyai University,

Romania; Geza Toth, Hungarian Central Statistical Office, Hungary; Andras Kovacs, Edutus College, Hungary; Istvan Papp and Levente Varga, Babes-Bolyai University, Romania

3:30-3:55 The Brain in SpaceZoltan Toroczkai, University of Notre

Dame, USA; Maria Ercsey-Ravasz, Babes-Bolyai University, Romania; Kenneth Knoblauch and Henry Kennedy, Inserm, France

Sunday, May 17

MS18Featured Minisymposium: Localized Pattern Formation in Reaction-diffusion Equations2:00 PM-4:00 PMRoom:Primrose B

Spatially localized states have recently brought to the spotlight of mathematical analysis of nonlinear PDEs via analysis of models exhibiting free energy and/or conservation. The purpose of this minisymposium is to generalize and discuss the state of the art in localized pattern formation theory through the reaction diffusion framework that is related to applications across a range of problems in chemistry and biology. The focus will be devoted to recent theories and computations of spatially localized patterns that can result from a number of different mechanisms, such as sub-critical bifurcations, homoclinic snaking, singular perturbations and semi-strong interaction asymptotics.

Organizer: Arik YochelisBen Gurion University Negev, Israel

2:00-2:25 The Origin of Finite Pulse Trains: Homoclinic Snaking in Excitable MediaArik Yochelis, Ben Gurion University Negev,

Israel; Edgar Knobloch, University of California, Berkeley, USA

2:30-2:55 Homoclinic Snaking Near a Codimension-two Turing-Hopf Bifurcation PointJustin C. Tzou, Dalhousie University, Canada;

Yiping Ma, University of Colorado Boulder, USA; Alvin Bayliss, Bernard J Matkowsky, and Vladimir A. Volpert, Northwestern University, USA

3:00-3:25 Slow Dynamics of Localized Spot Patterns for Reaction-Diffusion Systems on the SpherePhilippe H. Trinh, Princeton University, USA;

Michael Ward, University of British Columbia, Canada

3:30-3:55 Localised Solutions in a Non-Conservative Cell Polarization ModelNicolas Verschueren Van Rees and Alan

Champneys, University of Bristol, United Kingdom

Coffee Break4:00 PM-4:30 PMRoom:Golden Cliff

Sunday, May 17

MS17Featured Minisymposium: Stochastic Delayed Networks2:00 PM-4:00 PMRoom:Primrose A

Complex systems of the 21st century may exhibit rich dynamical behaviors due to complicated network structures, time delays and stochastic effects. Understanding the dynamics of such infinite dimensional dynamical systems requires new approaches and novel mathematical tools. This sections highlights the latest research result on the dynamics of networks where time delays arise due to finite-time information propagation between the nodes and stochasticity appears both in the state as well as in the time delays. Applications include neural networks, gene regulatory networks, and connected vehicle systems.

Organizer: Gabor OroszUniversity of Michigan, Ann Arbor, USA

2:00-2:25 Dynamics with Stochastically Delayed Feedback: Designing Connected Vehicle SystemsGabor Orosz and Wubing Qin, University

of Michigan, Ann Arbor, USA

2:30-2:55 New Mechanisms for Patterns, Transitions, and Coherence Resonance for Systems with Delayed FeedbackRachel Kuske and Chia Lee, University

of British Columbia, Canada; Vivi Rottschaefer, Leiden University, Netherlands

3:00-3:25 Synchronization of Degrade-and-Fire Oscillations Via a Common ActivatorWilliam H. Mather, Virginia Tech, USA; Jeff

Hasty and Lev S. Tsimring, University of California, San Diego, USA

3:30-3:55 On the Role of Stochastic Delays in Gene Regulatory NetworksMarcella Gomez and Matthew Bennett,

Rice University, USA; Richard Murray, California Institute of Technology, USA


Sunday, May 17

CP3Topics in Networks I4:30 PM-6:10 PMRoom:Ballroom III

Chair: Christian Bick, Rice University, USA

4:30-4:45 Analysis of Connected Vehicle Networks with Nontrivial Connectivity, a Modal Decomposition ApproachSergei S. Avedisov and Gabor Orosz,

University of Michigan, Ann Arbor, USA

4:50-5:05 Phase Response Properties of Collective Rhythms in Networks of Coupled Dynamical SystemsHiroya Nakao and Sho Yasui, Tokyo

Institute of Technology, Japan

5:10-5:25 Heterogeneities in Temporal Networks Emerging from Adaptive Social InteractionsTakaaki Aoki, Kagawa University, Japan;

Luis Rocha, Karolinska Institutet, Sweden; Thilo Gross, University of Bristol, United Kingdom

5:30-5:45 Simulating the Dynamics of College DrinkingBen G. Fitzpatrick, Jason Martinez, and

Elizabeth Polidan, Tempest Technologies LLC, USA

5:50-6:05 Integrating Hydrological and Waterborne Disease Network ModelsKarly Jacobsen and Michael Kelly, The

Ohio State University, USA; Faisal Hossain, University of Washington, USA; Joseph H. Tien, The Ohio State University, USA

Sunday, May 17

CP1Topics in Reaction-Diffusion Systems4:30 PM-6:30 PMRoom:Ballroom I

Chair: Petrus van Heijster, Queensland University of Technology, Australia

4:30-4:45 Defect Solutions in Reaction-Diffusion EquationsPeter van Heijster, Queensland University

of Technology, Australia

4:50-5:05 Reaction-Diffusion Equations with Spatially Distributed Hysteresis in Higher Spatial DimensionsMark J. Curran, Free University of Berlin,

Germany

5:10-5:25 Spatio-Temporal Dynamics of Heterogeneous Excitable MediaThomas Lilienkamp, Ulrich Parlitz, and

Stefan Luther, Max Planck Institute for Dynamics and Self-Organization, Germany

5:30-5:45 Existence of Periodic Solutions of the FitzHugh-Nagumo Equations for An Explicit Range of the Small ParameterAleksander Czechowski and Piotr

Zgliczyński, Jagiellonian University, Poland

5:50-6:05 Morse-Floer Homology for Travelling Waves in Reaction-Diffusion EquationsBerry Bakker, Jan Bouwe Van Den Berg,

and Robert van Der Vorst, VU University, Amsterdam, Netherlands

6:10-6:25 Low Dimensional Models of Diffusion and Reaction in Stratified Micro FlowsJason R. Picardo and Subramaniam

Pushpavanam, Indian Institute of Technology Madras, India

Sunday, May 17

CP2Topics in Pattern Formation I4:30 PM-6:30 PMRoom:Ballroom II

Chair: Jose Morales Morales, INRIA Rhone, France

4:30-4:45 Generalized Behavior of the Two-phase System in (1+1) DDavid A. Ekrut and Nicholas Cogan,

Florida State University, USA

4:50-5:05 Discrete Synchronization of Massively Connected Systems Using Hierarchical CouplingsCamille Poignard, Université de Nice,

Sophia Antipolis, France

5:10-5:25 Nonlinear Dynamics of Two-Colored FilamentsAlexey Sukhinin and Alejandro Aceves,

Southern Methodist University, USA

5:30-5:45 Scaling and Robustness of Two Component Morphogen Patterning SystemsMd. Shahriar Karim, Purdue University,

USA; Hans G. Othmer, University of Minnesota, USA; David Umulis, Purdue University, USA

5:50-6:05 Solitary Waves in the Excitable Discrete Burridge-Knopoff ModelJose Eduardo Morales Morales,

Guillaume James, and Arnaud Tonnelier, INRIA Rhone, France

6:10-6:25 Aspects and Applications of Generalized SynchronizationUlrich Parlitz, Max Planck Institute

for Dynamics and Self-Organization, Germany


Sunday, May 17

CP6Topics in Bifurcation Theory4:30 PM-6:30 PMRoom:Wasatch A

Chair: Shibabrat Naik, Virginia Tech, USA

4:30-4:45 Structuring and Stability of Solutions of the Static Cahn-Hilliard EquationSantiago Madruga, Universidad Politécnica

de Madrid, Spain; Fathi Bribesh, Zawia University, Libya; Uwe Thiele, University of Muenster, Germany

4:50-5:05 Sensitivity of the Dynamics of the General Rosenzweig-MacArthur Model to the Mathematical Form of the Functional Response: a Bifurcation Theory ApproachGunog Seo, Colgate University, USA; Gail

Wolkowicz, McMaster University, Canada

5:10-5:25 Continuation of Bifurcations in Physical ExperimentsDavid A. Barton, University of Bristol,

United Kingdom

5:30-5:45 Escape from Potential Wells in Multi-Degree of Freedom Systems: Phase Space Geometry and Partial ControlShibabrat Naik and Shane D. Ross, Virginia

Tech, USA

5:50-6:05 Experimental Verification of Criteria for Escape from a Potential Well in a Multi-degree of Freedom SystemShane D. Ross, Virginia Tech, USA; Amir

BozorgMagham, University of Maryland, College Park, USA; Lawrence Virgin, Duke University, USA

6:10-6:25 Periodic Social Niche ConstructionPhilip Poon, University of Wisconsin,

Madison, USA; David Krakauer and Jessica Flack, Wisconsin Institute for Discovery, USA

Sunday, May 17

CP4Topics in Computational Dynamical Systems I4:30 PM-6:30 PMRoom:Magpie A

Chair: Dinesh Kasti, Florida Atlantic University, USA

4:30-4:45 Expanded Mixed Finite Element Method for Generalized Forchheimer FlowsThinh T. Kieu, University of North Georgia,

USA; Akif Ibraguimov, Texas Tech University, USA

4:50-5:05 An Algorithmic Approach to Computing Lattice Structures of AttractorsDinesh Kasti and William D. Kalies,

Florida Atlantic University, USA; Robertus Vandervorst, Vrije Universiteit Amsterdam, The Netherlands

5:10-5:25 Prediction in ProjectionJoshua Garland and Elizabeth Bradley,

University of Colorado Boulder, USA

5:30-5:45 A Method for Identification of Spatially-Varying Parameters Despite Missing Data with Application to Remote SensingSean Kramer, Norwich University, USA;

Erik Bollt, Clarkson University, USA

5:50-6:05 Bifold Visualization of Dynamic NetworksYazhen Jiang, Joseph Skufca, and Jie Sun,

Clarkson University, USA

6:10-6:25 Sparse Sensing Based Detection of Dynamical Phenomena and Flow TransitionsPiyush Grover, Mitsubishi Electric

Research Laboratories, USA; Boris Kramer, Virginia Tech, USA; Petros Boufounos and Mouhacine Benosman, Mitsubishi Electric Research Laboratories, USA

Sunday, May 17

CP5Topics in Biological Dynamics I4:30 PM-6:10 PMRoom:Magpie B

Chair: Suma Ghosh, Pennsylvania State University, USA

4:30-4:45 A Mathematical Model for the Sexual Selection of Extravagant and Costly Mating DisplaysSara Clifton, Daniel Abrams, and Daniel

Thomas, Northwestern University, USA

4:50-5:05 A Model for Mountain Pine Beetle Outbreaks in An Age Structured Forest: Approximating Severity and Outbreak-Recovery Cycle PeriodJacob P. Duncan, James Powell, and Luis

Gordillo, Utah State University, USA; Joseph Eason, University of Utah, USA

5:10-5:25 Host-Mediated Responses on the Dynamics of Host-Parasite InteractionSuma Ghosh and Matthew Ferrari,

Pennsylvania State University, USA

5:30-5:45 Mathematical Models of Seasonally Migrating PopulationsJohn G. Donohue and Petri T. Piiroinen,

National University of Ireland, Galway, Ireland

5:50-6:05 Geometric Dissection of a Model for the Dynamics of Bipolar DisordersIlona Kosiuk, Max Planck Institute for

Mathematics in the Sciences, Germany; Ekaterina Kutafina, AGH University of Science and Technology, Poland; Peter Szmolyan, Vienna University of Technology, Austria


Sunday, May 17

CP7Topics in Mechanical Systems4:30 PM-6:10 PMRoom:Wasatch B

Chair: Thomas Ward, Iowa State University, USA

4:30-4:45 Numerical Simulations of Nonlinear Dynamics of Beams, Plates, and ShellsTimur Alexeev, University of California,

Davis, USA

4:50-5:05 Global Attractors for Quasilinear Parabolic-Hyperbolic Equations Governing Longitudinal Motions of Nonlinearly Viscoelastic RodsSuleyman Ulusoy, Zirve University, Turkey;

Stuart S Antman, University of Maryland, USA

5:10-5:25 Revision on the Equation of Nonlinear Vibration of the Cable with Large SagKun Wang, University of Macau, China

5:30-5:45 Control Strategies for Electrically Driven Flapping of a Flexible Cantilever Perturbed by Low Speed WindThomas Ward, Iowa State University, USA

5:50-6:05 A New Mathematical Explanation of What Triggered the Catastrophic Torsional Mode of the Tacoma Narrows BridgeGianni Arioli, Politecnico di Milano, Italy

Sunday, May 17

CP8Topics in Biological Dynamics II4:30 PM-6:30 PMRoom:Maybird

Chair: Luis Mier-y-Teran, Johns Hopkins Bloomberg School of Public Health, USA

4:30-4:45 Coexistence of Multiannual Attractors in a Disease Interaction Model: Whooping Cough RevisitedSamit Bhattacharyya, Matthew Ferrari,

and Ottar Bjornstad, Pennsylvania State University, USA

4:50-5:05 Order Reduction and Efficient Implementation of Nonlinear Nonlocal Cochlear Response ModelsMaurice G. Filo, University of California,

Santa Barbara, USA

5:10-5:25 Periodic Outbreaks in Models of Disease Transmission with a Behavioral ResponseWinfried Just, Ohio University, USA; Joan

Saldana, Universitat de Girona, Spain

5:30-5:45 Competition and Invasion of Dengue Viruses in Vaccinated PopulationsLuis Mier-y-Teran and Isabel Rodriguez-

Barraquer, Johns Hopkins Bloomberg School of Public Health, USA; Ira B. Schwartz, Naval Research Laboratory, USA; Derek Cummings, Johns Hopkins Bloomberg School of Public Health, USA

5:50-6:05 Examining Ebola Transmission Dynamics and Forecasting Using Identifiability and Parameter EstimationMarisa Eisenberg, University of Michigan,

USA

6:10-6:25 How Radiation-Induced Dedifferentation Influences Tumor HierarchyKimberly Fessel, Mathematical

Biosciences Institute, USA; John Lowengrub, University of California, Irvine, USA

Sunday, May 17

CP9Non-smooth Dynamical Systems4:30 PM-5:50 PMRoom:Superior A

Chair: John Hogan, Bristol Centre for Applied Nonlinear Mathematics and University of Bristol, United Kingdom

4:30-4:45 On the Use of Blow Up to Study Regularizations of Singularities of Piecewise Smooth Dynamical SystemsKristian Uldall Kristiansen, Technical

University of Denmark, Denmark; John Hogan, Bristol Centre for Applied Nonlinear Mathematics and University of Bristol, United Kingdom

4:50-5:05 C∞ Regularisation of Local Singularities of Filippov SystemsCarles Bonet and Tere M. Seara-Alonso,

Universitat Politecnica de Catalunya, Spain

5:10-5:25 Filippov Unplugged --- Part 1John Hogan, Bristol Centre for Applied

Nonlinear Mathematics and University of Bristol, United Kingdom; Martin Homer, Mike R. Jeffrey, and Robert Szalai, University of Bristol, United Kingdom

5:30-5:45 Filippov Unplugged - Part 2John Hogan, Bristol Centre for Applied

Nonlinear Mathematics and University of Bristol, United Kingdom; Martin Homer, Mike R. Jeffrey, and Robert Szalai, University of Bristol, United Kingdom


Sunday, May 17

CP11Topics in Feedback/Control/Optimization I4:30 PM-6:30 PMRoom:White Pine

Chair: Kathrin Flaßkamp, Northwestern University, USA

4:30-4:45 Computing Bisimulation Functions Using SoS Optimization and δ-Decidability over the RealsAbhishek Murthy, Philips Research North

America, USA; Md. Ariful Islam and Scott Smolka, Stony Brook University, USA; Radu Grosu, Vienna University of Technology, Austria

4:50-5:05 Chaos in Biological Systems with Memory and Its ControllabilityMark Edelman, Stern College for Women

and Courant Institute of Mathematical Sciences, New York University, USA

5:10-5:25 Odd-Number Limitation for Extended Time-Delayed Feedback ControlAndreas Amann and Edward Hooton,

University College Cork, Ireland

5:30-5:45 Approximate Controllability of An Impulsive Neutral Fractional Stochastic Differential Equation With Deviated Argument and Infinite DelaySanjukta Das and Dwijendra Pandey, Indian

Institute of Technology Roorkee, India

5:50-6:05 Mathematical Study of the Effects of Travel Costs on Optimal Dispersal in a Two-Patch ModelTheodore E. Galanthay, Ithaca College,

USA

6:10-6:25 Discrete-Time Structure-Preserving Optimal Ergodic ControlKathrin Flaßkamp and Todd Murphey,

Northwestern University, USA

Sunday, May 17

CP10Topics in Geometric and Nonlinear Dynamical Systems4:30 PM-6:30 PMRoom:Superior B

Chair: Colin J. Grudzien, University of North Carolina at Chapel Hill, USA

4:30-4:45 Tensor of Green of Coupled ThermoelastodynamicsBakhyt Alipova, University of Kentucky,

USA

4:50-5:05 Geometric Phase in the Hopf Bundle and the Sability of Non-Linear WavesColin J. Grudzien and Christopher Krt

Jones, University of North Carolina at Chapel Hill, USA

5:10-5:25 Error Assessment of the Local Statistical Linearization MethodLeo Dostal and Edwin Kreuzer, Hamburg

University of Technology, Germany

5:30-5:45 Curve Evolution in Second-Order Lagrangian SystemsRonald Adams and William D. Kalies,

Florida Atlantic University, USA; R.C.A.M van Der Vorst, Vrije Universiteit Amsterdam, The Netherlands

5:50-6:05 Periodic Eigendecomposition and Its Application in Nonlinear DynamicsXiong Ding and Predrag Cvitanovic,

Georgia Institute of Technology, USA

6:10-6:25 Computation of Cauchy-Green Strain Tensor Using Local RegressionShane D. Kepley and Bill Kalies, Florida

Atlantic University, USA

Sunday, May 17

CP12Topics in Atmospheric/Climate Dynamics and Related Themes4:30 PM-6:10 PMRoom:Primrose A

Chair: Miklos Vincze, Hungarian Academy of Sciences, Hungary

4:30-4:45 Gradual and Abrupt Regime Shifts in DrylandsYuval Zelnik, Ehud Meron, and Golan Bel,

Ben-Gurion University of the Negev, Israel

4:50-5:05 Baroclinic Instability in An Initially Stratified Rotating FluidMiklos P. Vincze, Hungarian Academy of

Sciences, Hungary; Patrice Le Gal, CNRS & Aix-Marseille Université, Marseille, France; Uwe Harlander, Brandenburg University of Technology, Germany

5:10-5:25 Modified Lorenz Equations for Rotating ConvectionJessica Layton, Jared P. Whitehead,

and Shane McQuarrie, Brigham Young University, USA

5:30-5:45 Empirical Validation of Conceptual Climate ModelsCharles D. Camp, Ryan Smith, and Andrew

Gallatin, California Polytechnic State University, USA

5:50-6:05 On the Geometry of Attractors in Ageostrophic Flows with Viscoelastic-Type Reynolds StressMaleafisha Stephen Tladi, University of

Limpopo, South Africa


Sunday, May 17

CP13Topics in Nonlinear Oscillators4:30 PM-6:10 PMRoom:Primrose B

Chair: Punit R. Gandhi, University of California, Berkeley, USA

4:30-4:45 Localized States in Periodically Forced SystemsPunit R. Gandhi, University of California,

Berkeley, USA; Cedric Beaume, Imperial College London, United Kingdom; Edgar Knobloch, University of California, Berkeley, USA

4:50-5:05 Multicluster and Traveling Chimera States in Nonlocal Phase-Coupled OscillatorsHsien-Ching Kao, Wolfram Research Inc.,

USA; Jianbo Xie and Edgar Knobloch, University of California, Berkeley, USA

5:10-5:25 Chimera States on the Route from Coherent State to a Rotating WaveTomasz Kapitaniak, Technical University of

Lodz, Poland

5:30-5:45 Onset and Characterization of Chimera States in Coupled Nonlinear OscillatorsLakshmanan Muthusamy, Bharathidasan

University, India

5:50-6:05 Emergent Rhythmic Behavior of Mixed-Mode Oscillations in Pulse-Coupled NeuronsAvinash J. Karamchandani, James

Graham, and Hermann Riecke, Northwestern University, USA

Dinner Break6:30 PM-8:00 PMAttendees on their own

DSWeb Editorial Board Meeting6:30 PM-8:00 PMRoom: Boardroom

Sunday, May 17Prize Presentations - Jürgen Moser and J. D. Crawford8:00 PM-8:15 PMRoom:Ballroom

J. D. Crawford Prize Recipient: Florin Diacu, University of Victoria, Canada

SP1Jürgen Moser Lecture - Dynamics and Data8:15 PM-9:00 PMRoom:Ballroom

Chair: Timothy Sauer, George Mason University, USA

This lecture highlights interdisciplinary interactions of dynamical systems theory. Experimental data and computer simulation have inspired mathematical discoveries, while resulting theory has made successful predictions and created new scientific perspectives. Nonlinear dynamics has unified diverse fields of science and revealed deep mathematical phenomena.

Examples involving

• One dimensional maps

• Numerical bifurcation analysis

• Multiple time scales

• Bursting and MMOs in neuroscience and chemistry

• Locomotion

are described, along with emerging areas having public impact.


Monday, May 18


MS5Structural and Functional Network Dynamics and Inference8:30 AM-10:30 AMRoom:Magpie B

Complex systems are ubiquitous in nature, yet there often remains a disconnect between models and real-world systems. This discrepancy can be manifest as limited knowledge about the ordinary and/or partial differential equations, the network encoding which variables interact, or both. System identification such as the inference of “structural” and “functional networks” is thus an unavoidable hurdle for the realistic modeling of many complex systems. We will study structural and functional networks arising in biological and physical systems as well as explore various network analyses such as community detection and motif extraction.

Organizer: Dane TaylorUniversity of North Carolina at Chapel Hill, USA

8:30-8:55 Causal Network Inference by Optimal Causation EntropyJie Sun and Erik Bollt, Clarkson University,

USA; Dane Taylor, University of North Carolina at Chapel Hill, USA

9:00-9:25 A Complex Networks Approach to Malaria’s Genetic Recombination DynamicsDaniel B. Larremore and Caroline Buckee,

Harvard School of Public Health, USA; Aaron Clauset, University of Colorado Boulder, USA

9:30-9:55 Combined Effects of Connectivity and Inhibition in a Model of Breathing RhythmogenesisKameron D. Harris, University of

Washington, USA; Tatiana Dashevskiy, Seattle Children’s Research Institute, USA; Eric Shea-Brown and Jan-Marino Ramirez, University of Washington, USA

10:00-10:25 Not-So-Random Graphs Through Wide MotifsPierre-Andre Noel, University of California,

Davis, USA


9:30-9:55 Symmetry Breaking and Synchronization Patterns in Networks of Coupled OscillatorsFrancesco Sorrentino, University of New

Mexico, USA; Aaron M. Hagerstrom, University of Maryland, USA; Louis M. Pecora, Naval Research Laboratory, USA; Thomas E. Murphy and Rajarshi Roy, University of Maryland, College Park, USA

10:00-10:25 Homeostasis As a Network InvariantMartin Golubitsky, The Ohio State

University, USA; Ian Stewart, University of Warwick, United Kingdom

Monday, May 18

MS20Structure-dynamics Relation in Networks of Coupled Dynamical Systems8:30 AM-10:30 AMRoom:Ballroom II

A fundamental question in studying coupled dynamical systems concerns the dynamics-structure relation -- how do the characteristics of the interactions between dynamical units determine the dynamical behavior of the system? After more than a decade of research on the structure of real networks, the problem of understanding this relation has become a major topic of interest in the dynamical systems community. This minisymposium will address this timely topic, focusing on network-dynamical phenomena, such as synchronization patterns, sensitive dependence of dynamical stability, and homeostasis, and using a range of mathematical tools from graph theory, linear algebra, group theory, and optimization.

Organizer: Francesco SorrentinoUniversity of New Mexico, USA

Organizer: Takashi NishikawaNorthwestern University, USA

8:30-8:55 Optimized Networks Have Cusp-like Dependence on Structural ParametersTakashi Nishikawa and Adilson E. Motter,


9:00-9:25 Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex NetworksLouis M. Pecora, Naval Research

Laboratory, USA; Francesco Sorrentino, University of New Mexico, USA; Aaron M. Hagerstrom, University of Maryland, USA; Rajarshi Roy and Thomas E. Murphy, University of Maryland, College Park, USA

Monday, May 18

MS19Patterns in Partial Differential Equations - Part II of II8:30 AM-10:30 AMRoom:Ballroom I

For Part 1 see MS1 Patterns play an important role in the dynamics of many dissipative and dispersive PDEs, posed on large or unbounded domains. This minisymposium will feature contributions that investigate intrinsically multi-dimensional aspects of the dynamics of patterns, including their existence, stability, instability, slow evolution, and interaction. Examples include interfaces between patterned and un-patterned state, point defects or vortices, and line defects. We expect to bring together researchers with a variety of backgrounds, employing a variety of techniques, such as diffusive and dispersive stability estimates, energy methods from the calculus of variations, or spatial dynamics and bifurcation methods.

Organizer: Keith PromislowMichigan State University, USA

Organizer: Noa KraitzmanMichigan State University, USA

8:30-8:55 Existence of Pearled Patterns in the Planar Functionalized Cahn-Hilliard EquationQiliang Wu, Michigan State University,

USA

9:00-9:25 Stability in Spatially Localized PatternsElizabeth J. Makrides and Bjorn

Sandstede, Brown University, USA

9:30-9:55 Reformulating Spectral Problems with the Krein MatrixTodd Kapitula, Calvin College, USA

10:00-10:25 A Geometric Approach to Stationary Defect SolutionsArjen Doelman, Leiden University,

Netherlands; Peter van Heijster, Queensland University of Technology, Australia; Feng Xie, Leiden University, Netherlands

continued in next column


Monday, May 18

MS21Ocean-in-the-loop: Towards Real-Time Monitoring in Geophysical Flows - Part II of II8:30 AM-10:30 AMRoom:Ballroom III

For Part 1 see MS3 Improved modeling and prediction of fluid dynamics is needed to better understand ocean and atmospheric transport along with associated applications including contaminant dispersion, environmental modeling, and underwater acoustic propagation. Major recent advances in closed-loop adaptive sampling, Lagrangian data assimilation, uncertainty quantification, and phase space transport are providing improved understanding of transport phenomena. The purpose of this minisymposium is to expose the audience to recent progress and developments, as well as to bring together researchers developing new mathematical methods and applications for use in understanding flow transport.

Organizer: Eric ForgostonMontclair State University, USA

Organizer: Ani HsiehDrexel University, USA

8:30-8:55 Optimal Control in Lagrangian Data AssimilationDamon Mcdougall, University of Texas

at Austin, USA; Richard O. Moore, New Jersey Institute of Technology, USA

9:00-9:25 A Hybrid Particle-Ensemble Kalman Filter for High Dimensional Lagrangian Data AssimilationElaine Spiller, Marquette University, USA;

Laura Slivinski, Woods Hole Oceanographic Institute, USA; Amit Apte, TIFR Centre, Bangalore, India

9:30-9:55 A Multi Agent Control Strategy for Sampling Uncertain Spatio-Temporally Varying Flow FieldsAxel Hackbarth and Edwin Kreuzer,

Hamburg University of Technology, Germany

10:00-10:25 Bayesian Nonlinear Assimilation for Eulerian Fields and Lagrangian TrajectoriesPierre Lermusiaux, Massachusetts Institute

of Technology, USA

Monday, May 18

MS22Geometric Mechanics and Applications8:30 AM-10:30 AMRoom:Magpie A

This minisymposium will focus on the application of geometric methods to dynamical systems originating in mechanicals. The geometric viewpoint provides a unified and systematic framework to address a broad range of problems, including control, numerical integration, and qualitative dynamics, for both finite- and infinite-dimensional systems. In particular, topics represented include the geometric optimal control of mechanical systems, stability analysis, variational principles, the use of momentum maps, and variational integrators. This minisymposium provides a unique opportunity for mathematicians, applied mathematicians, and engineers to come together and explore their common interest in the geometric approach to mechanics.

Organizer: Vakhtang PutkaradzeUniversity of Alberta, Canada

8:30-8:55 The Geometry of the Toda Lattice MapAnthony M. Bloch, University of Michigan,

USA

9:00-9:25 Dynamics and Optimal Control of Flexible Solar Updraft TowersVakhtang Putkaradze, University of

Alberta, Canada

9:30-9:55 Geodesic Finite Elements on Symmetric Spaces and Their Applications to Multisymplectic Variational IntegratorsPhillip Grohs, ETH Zürich, Switzerland;

Melvin Leok, Joe Salamon, and John Moody, University of California, San Diego, USA

10:00-10:25 Hamel’s Formalism for Infinite-Dimensional Mechanical SystemsDmitry Zenkov, North Carolina State

University, USA

Monday, May 18

MS24Nontwist Hamiltonian systems: Theory and Applications8:30 AM-10:30 AMRoom:Wasatch A

In recent years, more and more physical systems have been found that can be modeled by Hamiltonians that locally violate a non-degeneracy condition leading to the appearance of so-called shearless invariant tori which act as particularly robust transport barriers in phase space. This minisymposium brings together researchers from physics and applied mathematics to present the latest developments and applications in the subject of nontwist Hamiltonian systems. Recent numerical studies of breakup and emergence of shearless tori and applications in plasma physics will be discussed.

Organizer: Alexander WurmWestern New England University, USA

Organizer: P. J. MorrisonUniversity of Texas at Austin, USA

8:30-8:55 Breakup of Shearless Tori and Reconnection in the Piecewise-Linear Standard Nontwist MapAlexander Wurm, Western New England

University, USA

9:00-9:25 Nontwist Worm MapCaroline G. L. Martins and P. J. Morrison,

University of Texas at Austin, USA; J. D. Szezech, Universidade Estadual de Ponta Grossa, Brazil; I. L. Caldas, Universidade de Sao Paulo, Brazil

9:30-9:55 Breakup of Tori in Multiharmonic Nontwist Standard MapsAdam M. Fox, Western New England

University, USA; James D. Meiss, University of Colorado Boulder, USA

10:00-10:25 Influence of Finite Larmor Radius on Critical Parameters for Invariant Curves Break Up in Area Preserving Maps Models of ExB Chaotic TransportJulio Fonseca, University of Sao Paulo,

Brazil; Diego Del-Castillo-Negrete, Oak Ridge National Laboratory, USA; Iberê L. Caldas, Universidade de Sao Paulo, Brazil


Monday, May 18

MS27Analysis of Network Dynamical Systems8:30 AM-10:30 AMRoom:Superior A

Many real world dynamical systems admit a nontrivial network structure. This special structure often makes these systems behave in an unexpected way. Networks can for example synchronise, support anomalous bifurcations, admit robust heteroclinic cycles, display chimera states, etc. In other words: dynamical behaviour that is classically considered “degenerate” and hence “irrelevant”, turns out to be generic in the context of networks, and can thus be important for applications. In this minisymposium, we present a number of recent insights in the analysis of networks that may be used to understand and predict their dynamical behaviour.

Organizer: Bob RinkVU University, Amsterdam, Netherlands

Organizer: Eddie NijholtVU University, Amsterdam, Netherlands

8:30-8:55 Classifying Bifurcations in Coupled Cell NetworksEddie Nijholt, Bob Rink, and Jan Sanders,

VU University, Amsterdam, Netherlands

9:00-9:25 Pulse Bifurcations in Stochastic Neural FieldsZachary Kilpatrick, University of Houston,

USA; Gregory Faye, École des Hautes Etudes en Sciences Sociales, France

9:30-9:55 Dynamics of Asynchronous NetworksChristian Bick, Rice University, USA;

Michael Field, Imperial College London, United Kingdom; Anushaya Mohapatra, Oregon State University, USA

10:00-10:25 Dynamics of Heterogeneous Networks: Reductions and Coherent BehaviourTiago Pereira, Universidade de Sao Paulo,

Brazil; Matteo Tanzi and Sebastian van Strien, Imperial College London, United Kingdom

Monday, May 18

MS26Experiments on Transport in Multi-scale Fluid Systems8:30 AM-10:30 AMRoom:Maybird

Transport in fluid systems is mainly investigated by theoretical and numerical methods. Experimental studies lag behind yet are crucial both for validation purposes and for investigation of phenomena that are beyond theory and simulations. The aims of these investigations range from validation of fundamental transport phenomena to bridging the gap from dynamical-systems concepts to (industrial) applications. This mini-symposium highlights the essential role of laboratory experiments in comprehensive transport studies of multi-scale systems, which are almost the only class of flows that allows analytical description and presents a natural meeting point for experiments, simulations and theory.

Organizer: Michel SpeetjensEindhoven University of Technology, Netherlands

Organizer: Dmitri VainchteinTemple University, USA

8:30-8:55 Chaotic Mixing and Transport BarriersThomas H. Solomon, Bucknell University,

USA

9:00-9:25 How Small a Thought: Design of Mixing and Separation Processes with Dynamical SystemsGuy Metcalfe, CSIRO, Australia

9:30-9:55 3D Chaotic Advection in Langmuir CellsLarry Pratt and Irina Rypina, Woods Hole

Oceanographic Institute, USA

10:00-10:25 Experimental Investigation of Fundamental Lagrangian Transport PhenomenaMichel Speetjens, Eindhoven University of

Technology, Netherlands

Monday, May 18

MS25Rhythmic Dynamics of Minimal Neuronal Networks8:30 AM-10:30 AMRoom:Wasatch B

Recent trends in mathematical and computational neuroscience have led to studies of increasingly larger networks. However, there are still many fundamental questions related to the dynamics of rhythmic networks that are best suited to be addressed in the context of small and minimal models. Speakers in this minisymposium will focus on questions that involve multiple time scales, the detection of synchrony and the coordination of neural activity in the context of central pattern generators and more general brain networks. A primary goal is to use mathematical modeling to identify biological mechanisms that underlie the existence and control of rhythms. Because of the minimal nature of the models considered, mathematical findings can fairly clearly be correlated to biological mechanisms.

Organizer: Amitabha BoseNew Jersey Institute of Technology, USA

8:30-8:55 The Role of Voltage-Dependent Electrical Coupling in the Control of OscillationsChristina Mouser, William Patterson

University, USA; Farzan Nadim and Amitabha Bose, New Jersey Institute of Technology, USA

9:00-9:25 Understanding and Distinguishing Multiple Time Scale OscillationsYangyang Wang and Jonathan E. Rubin,

University of Pittsburgh, USA

9:30-9:55 The Essential Role of Phase Delayed Inhibition in Decoding Synchronized OscillationsBadal Joshi, California State University, San

Marcos, USA; Mainak Patel, College of William & Mary, USA

10:00-10:25 Neural Mechanisms of Limb Coordination in Crustacean SwimmingTim Lewis, University of California, Davis,

USA


Monday, May 18

MS30Network Synchronization in Mechanical Systems and Beyond - Part II of II8:30 AM-10:30 AMRoom:Primrose A

For Part 1 see MS12 This minisymposium focuses on the role of synchronization, coordination, and dynamical consensus in mechanical systems and beyond. Examples range from bridges and mechanical pendula to self-organizing networks of moving agents, with application in robotics and animal behavior. This minisymposium aims at various theoretical and experimental aspects of synchrony-induced phenomena and their control and brings together applied mathematicians and mechanical engineers.

Organizer: Igor BelykhGeorgia State University, USA

Organizer: Maurizio PorfiriPolytechnic Institute of New York University, USA

8:30-8:55 Synchronization in Dynamical Networks of Noisy Nonlinear Oscillators, Or Collective Behavior of ZebrafishViolet Mwaffo and Ross Anderson, New

York University Polytechnic, USA; Maurizio Porfiri, Polytechnic Institute of New York University, USA

9:00-9:25 Synchronization of a Nonlinear Beam Coupled with Deformable SubstratesDavide Spinello, University of Ottawa,

Canada

9:30-9:55 A Self-Organising Distributed Strategy for Optimal Synchronisation of Networked Mechanical SystemsLouis Kempton, Guido Hermann, and

Mario Di Bernardo, University of Bristol, United Kingdom

10:00-10:25 Synchronization Control of Electrochemical Oscillator Assemblies by External InputsAnatoly Zlotnik, Los Alamos National

Laboratory, USA; Istvan Z. Kiss and Raphael Nagao, Saint Louis University, USA; Jr-Shin Li, Washington University, St. Louis, USA

Monday, May 18

MS29Multiscale Models to Understand the Social and Physical World - Part II of II8:30 AM-10:30 AMRoom:White Pine

For Part 1 see MS11 The scientific community has developed a rich and diverse library of mathematical models capable of capturing complex processes and interactions over a broad range of scales in space and time. In this session, we feature a variety of researchers exploring the application of mathematical models to the social and physical world. The topics of this session cover several scales, from interacting particles to population models to PDEs, and include both stochastic and deterministic models. Talks will address applications such as earthquakes, swimming microorganisms, and human crowd dynamics.

Organizer: Alethea BarbaroCase Western Reserve University, USA

Organizer: Brittany EricksonPortland State University, USA

8:30-8:55 Population Models Applied to Model the Pregnancy to Labor TransitionDouglas Brubaker, Alethea Barbaro, Mark

Chance, and Sam Mesiano, Case Western Reserve University, USA

9:00-9:25 Stochastic Fluctuations in Suspensions of Swimming MicroorganismsPeter R. Kramer, Yuzhou Qian, and Patrick

Underhill, Rensselaer Polytechnic Institute, USA

9:30-9:55 A Model for Riot Dynamics: Shocks, Diffusion and ThresholdsNancy Rodriguez-Bunn, University of

North Carolina at Chapel Hill, USA; Henri Berestycki and Jean-Pierre Nadal, CNRS, France

10:00-10:25 Crowd Modeling: How Can People Respond to FearJesus Rosado Linares, Universidad

de Buenos Aires, Argentina; Alethea Barbaro, Case Western Reserve University, USA; Andrea L. Bertozzi, University of California, Los Angeles, USA

Monday, May 18

MS28Simple Systems with Complex Dynamics8:30 AM-10:30 AMRoom:Superior B

Lab experiments can often be very costly as they may require expensive equipment. However, research in dynamical systems can still be done using simple table top experiments at low cost. Many of these systems may seem extremely simple and mundane in set up, yet they can be very rich in their dynamics. In this mini-symposium, we present four table top experiments involving mechanical, chemical and electrical oscillators and show how they can produce complex phenomena such as synchronization, period doubling bifurcation and chaos. We also demonstrate how these systems can be studied mathematically and numerically.

Organizer: Andrea J. WelshGeorgia Institute of Technology, USA

8:30-8:55 Period Doubling in the Saline OscillatorDiandian Diana Chen and Flavio

Fenton, Georgia Institute of Technology, USA

9:00-9:25 Oscillatory Dynamics of the CandelatorGreg A. Byrne, Mary Elizabeth Lee,

and Flavio Fenton, Georgia Institute of Technology, USA

9:30-9:55 Synchronization Patterns in Simple Networks of Optoelectronic OscillatorsBriana Mork, Gustavus Adolphus College,

USA; Kate Coppess, University of Michigan, Ann Arbor, USA; Caitlin R. S. Williams, Washington and Lee University, USA; Aaron M. Hagerstrom and Joseph Hart, University of Maryland, USA; Thomas E. Murphy, University of Maryland, College Park, USA; Rajarshi Roy, University of Maryland, USA

10:00-10:25 Noise-Induced Transitions in Bistable Tunnel Diode CircuitsStephen Teitsworth, Yuriy Bomze,

Steven Jones, and Ryan McGeehan, Duke University, USA


Monday, May 18

MS32Energy Transfer and Harvesting in Nonlinear Systems - Part I of II1:15 PM-3:15 PMRoom:Ballroom I

For Part 2 see MS45 The minisymposium will focus on recent developments and challenges related to energy transfer and harvesting in nonlinear systems. Special attention will be paid to rapidly developing research field of nonsmooth systems. Topics will include, but will not be limited to:

• New results in the classical problem of divergent vs convergent heat conduction in models of atomic lattices;

• Description of wave initiation, propagation and mitigation in granular systems;

• Nonlinear targeted energy transfer in systems with strongly nonlinear attachments

• Applications of strong and non-smooth nonlinearities for efficient energy harvesting.

Organizer: Oleg GendelmanTechnion Israel Institute of Technology, Israel

Organizer: Alexander VakakisUniversity of Illinois, USA

1:15-1:40 Convergent Heat Conduction in One-Dimensional Lattices with DissociationOleg Gendelman, Technion Israel Institute

of Technology, Israel; Alexander Savin, Institute of Chemical Physics, Moscow, Russia

1:45-2:10 Stochastic Closure Schemes for Bi-stable Energy Harvesters Excited by Colored NoiseThemistoklis Sapsis and Han Kyul Joo,

Massachusetts Institute of Technology, USA

2:15-2:40 Bistable Nonlinear Energy Sink Coupled System for Energy Absorption and HarvestingFrancesco Romeo, University of Rome

La Sapienza, Italy; Giuseppe Habib, University of Liege, Belgium

2:45-3:10 Acceleration of Charged Particles in the Presence of FluctuationsAfrica Ruiz Mora and Dmitri Vainchtein,

Temple University, USA

Monday, May 18

IP2Mathematics of Crime11:00 AM-11:45 AMRoom:Ballroom

Chair: Michelle Girvan, University of Maryland, USA

There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems, especially for young researchers. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety of mathematical methods that are applicable to such problems. We will review recent work on agent based models, methods in linear and nonlinear partial differential equations, variational methods for inverse problems and statistical point process models. From an application standpoint we will look at problems in residential burglaries and gang crimes. Examples will consider both “bottom up’ and ‘top down’ approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory.

Andrea L. BertozziUniversity of California, Los Angeles, USA

Lunch Break11:45 AM-1:15 PMAttendees on their own

Monday, May 18

MS31Extreme Events: Modeling, Analysis, Prediction, and Control8:30 AM-10:30 AMRoom:Primrose B

Extreme events are considered to be rare events characterized by a large impact on a particular system which is measured in terms of some observable or order parameter. The aim of this minisymposium is to discuss the mechanisms of generation of extreme events as well as their prediction and control in different system classes which are relevant to different applications in nature. The system classes covered by this minisymposium are excitable population dynamical systems, coupled systems, stochastic multistable systems as well as small-world networks of excitable units of FitzHugh Nagumo type.

Organizer: Ulrike FeudelUniversity of Oldenburg, Germany

Organizer: Klaus LehnertzUniversity of Bonn, Germany

8:30-8:55 Extreme Events in Nature: Harmful Algal BloomsUlrike Feudel, University of Oldenburg,

Germany; Subhendu Chakraborty, DTU Aqua, Denmark; Cornelius Steinbrink, Rajat Karnatak, and Helmut Hillebrand, University of Oldenburg, Germany

9:00-9:25 Extreme Events on Small-World Networks of Excitable UnitsGerrit Ansmann and Klaus Lehnertz,

University of Bonn, Germany; Ulrike Feudel, University of Oldenburg, Germany

9:30-9:55 Extreme Events in Stochastic Multistable SystemsAlexander N. Pisarchik, Technical University

of Madrid, Spain; Ricardo Sevilla-Escoboza, Guillermo Huerta-Cuellar, and Rider Jaimes-Reátegui, Universidad de Guadalajara, Mexico

10:00-10:25 Forecasting and Controlling Dragon-King Events in Coupled Dynamical SystemsDaniel J. Gauthier, Duke University,

USA; Hugo Cavalcante and Marcos Oria, Universidade Federal da Paraiba, Brazil; Didier Sornette, ETH Zürich, Switzerland; Ed Ott, University of Maryland, USA

Coffee Break10:30 AM-11:00 AMRoom:Golden Cliff


Monday, May 18

MS35Dynamics of Inertial Particles in Flows1:15 PM-3:15 PMRoom:Magpie A

The dynamics of particles in fluid flows is of fundamental importance in a wide range of scientific problems. Heavy particles respond in intricate ways to fluid-velocity fluctuations. Recently there has been substantial progress in understanding the dynamics of such particles by analysing simplified mathematical models. Most models neglect the effect of fluid inertia although it can have a substantial effect in certain cases. The goal of this minisymposium is to discuss recent developments in understanding the role of fluid inertia upon the motion of particles suspended in steady and in turbulent flows.

Organizer: Bernhard MehligUniversity of Gothenburg, Sweden

1:15-1:40 The Effect of Particle and Fluid Inertia on the Dynamics of Particles in FlowsBernhard Mehlig, University of Gothenburg,

Sweden

1:45-2:10 Effect of Fluid and Particle Inertia on the Dynamics and Scaling of Ellipsoidal Particles in Shear FlowTomas Rosen, KTH Royal Institute of

Technology, Sweden; Yusuke Kotsubo, Tokyo University, Japan; Cyrus Aidun, Georgia Institute of Technology, USA; Fredrik Lundell, KTH Stockholm, Sweden

2:15-2:40 Inertia Effects in the Dynamics of Spherical and Non-Spherical Objects at Low Reynolds NumberFabien Candelier, Aix-Marseille Université,

France

2:45-3:10 Influence of the History Force on Inertial Particle Advection: Gravitational Effects and Horizontal DiffusionKsenia Guseva and Ulrike Feudel, University

of Oldenburg, Germany; Tamas Tel, Eötvös Loránd University, Hungary

Monday, May 18

MS34Mathematical Models of Cancer Development and Treatment1:15 PM-3:15 PMRoom:Ballroom III

Cancer develops in stages from incipience to metastasis, often followed by the emergence of drug resistance and evasion of the immune response. Understanding cancer progression and interaction with treatments will lead to insights into cancer therapy by aiding the design of innovative strategies that include and combine chemotherapy, virotherapy, immunotherapy, and other approaches. Current mathematical models seek to understand cancer deterministically and stochastically from the level of populations to individual cells. This minisymposium will bring together speakers who are applying a variety of mathematical and computational approaches to consider various stages of cancer development and treatment.

Organizer: Joanna WaresUniversity of Richmond, USA

Organizer: Peter S. KimUniversity of Sydney, Australia

1:15-1:40 How Much and How Often? Mathematical Models of Cancer Vaccine DeliveryAmi Radunskaya, Pomona College, USA

1:45-2:10 A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length HierarchiesGeorgi Kapitanov, University of Iowa,

USA

2:15-2:40 A Cell Population Model Structured by Cell Age Incorporating Cell-cell AdhesionGlenn Webb, Vanderbilt University, USA

2:45-3:10 Mathematical Models of the Treatment of Chronic Lymphocytic Leukemia with Ibrutinib and the Development of Drug ResistanceDominik Wodarz, University of California,

Irvine, USA

Monday, May 18

MS33Rare Events in Stochastic Systems1:15 PM-3:15 PMRoom:Ballroom II

A pivotal goal in the analysis of dynamical systems is the prediction and qualitative description of long-term behavior. In deterministic systems, this is often accomplished via bifurcation analysis and the identification of invariant motions, usually considering the behavior of orbits. Most practical systems however are noisy, and even in the presence of small noise a stochastic system will exhibit events that cannot be described by deterministic dynamics alone. The rarity of such events necessitates specialized tools and approaches to study them. This minisymposium will focus on recent advancements in the methods to investigate rare events as well as intriguing applications of these methods.

Organizer: Christoffer R. HeckmanUniversity of Colorado Boulder, USA

Organizer: Ira B. SchwartzNaval Research Laboratory, USA

1:15-1:40 Rare Events in Stochastic Dynamical Systems with Delay: From Random Switching to ExtinctionsIra B. Schwartz, Naval Research

Laboratory, USA; Thomas W. Carr, Southern Methodist University, USA; Lora Billings, Montclair State University, USA; Mark Dykman, Michigan State University, USA

1:45-2:10 Rare Event Extinction on Stochastic NetworksLeah Shaw, College of William & Mary,

USA; Brandon S. Lindley and Ira B. Schwartz, Naval Research Laboratory, USA

2:15-2:40 Influence of Periodic Modulation in Extreme Optical PulsesCristina Masoller, Universitat Politecnica

de Catalunya, Spain

2:45-3:10 Models of Large Deviations and Rare Events for Optical PulsesWilliam Kath, Northwestern University,

USA


Monday, May 18

MS38Spatial Organization of Biochemical Dynamics Within and Between Cells1:15 PM-3:15 PMRoom:Wasatch B

Recent advances in imaging of biochemical processes has revealed spatial organization of the underlying processes, which were previously assumed homogenous or well-mixed. We explore modeling methods to describe the spatial organization of these processes within and between cells. Approaches include PDE and ODE based models, matched asymptotic expansions, dominant balance analysis, and agent based modeling. The symposium includes a range of applications: improved efficiency of metabolic reactions through cellular spatial organization, quorum sensing in biofilms, cell-fate decisions due to signaling gradients, and the effect of the micro environment on drug resistance in cancer cells.

Organizer: Niall M. ManganMassachusetts Institute of Technology, USA

1:15-1:40 Organization of Metabolic Reactions for Improved Efficiency: Carbon Fixation and Bioengineering ApplicationsNiall M. Mangan, Massachusetts Institute

of Technology, USA

1:45-2:10 A 3D Model of Cell Signal TransductionDavid Iron, Dalhousie University, Canada

2:15-2:40 Synthetic Genetic Circuits for Spatial PatterningPaul Steiner, University of California, San

Diego, USA

2:45-3:10 An Spatial Model of Anti-Cancer Drug Resistance: the Role of the Micro-EnvironmentKerri-Ann Norton, Johns Hopkins

University, USA; Kasia Rejniak, H. Lee Moffitt Cancer Center & Research Institute, USA; Jana Gevertz, The College of New Jersey, USA; Judith Pérez-Velázquez, Helmholtz Zentrum München, Germany; Zahra Aminzare, Rutgers University, USA; Alexandria Volkening, Brown University, USA

Monday, May 18

MS37Guided Approaches to Ocean Data Assimilation Incorporating Uncertainty and Observability1:15 PM-3:15 PMRoom:Wasatch A

Ocean dynamics strongly drive transport and ecological balances at all spatiotemporal scales, influencing seasonal and operational forecasts for commerce and defense. Prediction of ocean dynamics is challenging due to sparsity and inhomogeneity of observations, as well as nonlinearity of dynamics and model errors contributing to uncertainty. These challenges may be met through data assimilation techniques that properly incorporate uncertainty, along with the use of distributed sampling platforms for in situ sampling. This session focuses on guided data assimilation for incorporating uncertainty into observing system design. To improve overall forecast skill, we address questions related to observability, identification of coherent flow structures, and desirable sampling trajectories.

Organizer: Derek A. PaleyUniversity of Maryland, USA

1:15-1:40 A Quantitative Measure of Observability for Data AssimilationsWei Kang, Naval Postgraduate School,

USA; Sarah King and Liang Xu, Naval Research Laboratory, USA

1:45-2:10 Probabilistic Approach to Deployment Strategy in Lagrangian Data AssimilationKayo Ide, University of Maryland, College

Park, USA

2:15-2:40 Multivehicle Motion Planning in the Presence of Ocean EddiesFrank D. Lagor and Derek A. Paley,

University of Maryland, USA

2:45-3:10 Bayesian Nonlinear Smoothing and Mutual Information for Adaptive SamplingTapovan Lolla and Pierre Lermusiaux,


Monday, May 18

MS36Theory and Applications of Nonsmooth Dynamics in Physical Systems - Part I of II1:15 PM-3:15 PMRoom:Magpie B

For Part 2 see MS49 This minisymposium will provide a mix of talks featuring theoretical developments in nonsmooth systems as well as talks featuring applications with nonsmooth dynamics. In either case, physical applications provide the motivation for mathematical exploration. Additionally, the minisymposium will blend talks appropriate for a broad audiences and talks geared at experts. To that point, the minisymposium will begin with the very general “How nonsmooth are the Earth sciences?” which will set the stage for the rest of the speakers. Other talks will discuss issues such as generalized bifurcations, canard phenomena, synchronization, and the new area of resilience.

Organizer: Andrew RobertsCornell University, USA

Organizer: Esther WidiasihUniversity of Hawaii, West Oahu, USA

1:15-1:40 How Nonsmooth Are the Earth Sciences?Chris Budd and Tim J. Dodwell, University

of Bath, United Kingdom

1:45-2:10 The Search for Glacial Cycles: A Quasiperiodically Forced Nonsmooth System in a Conceptual Climate ModelEsther Widiasih, University of Hawaii,

West Oahu, USA; James Walsh, Oberlin College, USA; Richard McGehee and Jonathan Hahn, University of Minnesota, USA

2:15-2:40 Analysis of an Arctic Sea Ice Model in a Nonsmooth LimitKaitlin Hill and Mary Silber, Northwestern

University, USA

2:45-3:10 Mathematical Quantifications of ResilienceAlanna Hoyer-Leitzel, Bowdoin College,

USA


Monday, May 18

MS41Renewable Energy and Power Grids: Their Mathematical Characterizations - Part I of II1:15 PM-3:15 PMRoom:Superior B

For Part 2 see MS54 It is our social demand to introduce more renewable energy resources into power grids. However, because renewable energy outputs fluctuate according to weather conditions, we need to control and/or optimize power grids so that we can keep the voltage and frequency as constant and stable. Here we put together some recent advances to achieve this need mathematically. This need for more renewables makes us to combine several fields of mathematics together such as dynamical systems theory, control theory and complex network theory. This need also brings us into new research directions, which will turn our mathematical tools more practical.

Organizer: Yoshito HirataUniversity of Tokyo, Japan

Organizer: Jun-ichi ImuraTokyo Institute of Technology, Japan

Organizer: Juergen KurthsPotsdam Institute for Climate Impact Research and Humboldt University Berlin, Germany

1:15-1:40 Time Series Prediction for Renewable Energy ResourcesYoshito Hirata, University of Tokyo, Japan;

Kazuyuki Aihara, JST/University of Tokyo, Japan; Hideyuki Suzuki, University of Tokyo, Japan

1:45-2:10 Analysis of Systems in Buildings Using Koopman Operator MethodsMichael Georgescu, University of

California, Santa Barbara, USA

Monday, May 18

MS40The Behavior of Autonomous Agents in Diverse Applications1:15 PM-3:15 PMRoom:Superior A

Many different applications, such as the swarming of insects, the interaction of cells, and the flow of traffic, when studied mathematically, naturally take the form of agent-based models. The diversity of perspectives on the behavior of autonomous agents across these fields provides an opportunity for a cross-fertilization of ideas and techniques. The goal of this minisymposium is to capitalize on the differences between these applications, in the context of agent-based models and their analyses, to ignite more ideas and better answer the questions that arise in many fields.

Organizer: Paul A. CarterBrown University, USA

Organizer: Alexandria VolkeningBrown University, USA

1:15-1:40 Modeling Stripe Formation in ZebrafishAlexandria Volkening and Bjorn


1:45-2:10 Predator-Swarm InteractionsTheodore Kolokolnikov, Dalhousie

University, Canada

2:15-2:40 Non-Standard Travelling Waves in Traffic and Pedestrian Flow ModelsPaul Carter, Brown University, USA; Peter

Leth Christiansen, Technical University of Denmark, Denmark; Yuri Gaididei, Bogolyubov Institute for Theoretical Physics, Ukraine; Carlos Gorria, University of the Basque Country, Spain; Christian Marschler, Technical University of Denmark, Denmark; Bjorn Sandstede, Brown University, USA; Mads Peter Soerensen and Jens Starke, Technical University of Denmark, Denmark

2:45-3:10 Topological Data Analysis of Biological Aggregation ModelsChad M. Topaz, Lori Ziegelmeier, and Tom

Halverson, Macalester College, USA

Monday, May 18

MS39Reduced Dynamical Models and Their Applications - Part I of II1:15 PM-3:15 PMRoom:Maybird

For Part 2 see MS52 The purpose is to present a cross-section of leading-edge research on the development, analysis, numerical solution, visualization and applications of reduced dynamical systems models. These models may arise via simplification of form of infinite-dimensional systems, reduction in cardinality of the dimension, possibly by restriction to invariant submanifolds, and ad hoc techniques based upon focusing on certain combinations of variables. Among the reductions to be discussed are simplified infinite-dimensional models for granular flows, reduced dimensional models via extensions of the zero derivative principle, discrete dynamical systems reductions for logical circuits and ecological models, and discrete integrable reductions of continuum models.

Organizer: Denis BlackmoreNew Jersey Institute of Technology, USA

Organizer: Anthony RosatoNew Jersey Institute of Technology, USA

1:15-1:40 Reduced Models for Granular and Ecological DynamicsDenis Blackmore, Anthony Rosato,

and Hao Wu, New Jersey Institute of Technology, USA

1:45-2:10 On the Calogero Type Integrable Discretization of Nonlinear Dynamical SystemsAnatolij Prykarpatski, AGH University of

Science and Technology, Poland

2:15-2:40 A Scheme for Modeling and Analyzing the Dynamics of Logical CircuitsAminur Rahman, New Jersey Institute of

Technology, USA

2:45-3:10 Collective Coordinates as Model Reduction for Nonlinear Wave InteractionsIvan C. Christov, Los Alamos National

Laboratory, USAcontinued on next page


Monday, May 18

MS43Applications of Exactly Solvable Chaos1:15 PM-3:15 PMRoom:Primrose A

Recent work on certain hybrid dynamical systems, containing linear continuous-time differential equations coupled to a discrete-time switching condition, revealed a new class of chaos that exhibits a quasi-linear nature. These systems generate chaotic waveforms as typical solutions that have an exact analytic description as a linear convolution of a fixed basis function and a symbolic dynamics. As a consequence, for the first time, chaotic waveforms could be dissected and analyzed using the tools of linear analysis. This minisymposium explores physical and technological applications of exactly solvable chaotic oscillators.

Organizer: Lucas IllingReed College, USA

Organizer: Ned J. CorronUS Army RDECOM, USA

1:15-1:40 Communication Waveforms and Exactly Solvable ChaosNed J. Corron and Jonathan N. Blakely, US

Army RDECOM, USA

1:45-2:10 A Pseudo-Matched Filter for Solvable ChaosSeth D. Cohen, Miltec Corp., USA

2:15-2:40 Methods for Implementing Exactly Solvable Chaos in Electronic CircuitsAubrey N. Beal and Robert Dean, Auburn

University, USA

2:45-3:10 Exactly Solvable Chaos in An Electromechanical OscillatorLucas Illing, Reed College, USA

Monday, May 18

MS42Extensions and Applications of Dynamic Mode Decomposition - Part I of II1:15 PM-3:15 PMRoom:White Pine

For Part 2 see MS55 Dynamic mode decomposition (DMD) is a powerful method that identifies spatial-temporal coherent structures in high-dimensional datasets. Introduced less than a decade ago, it has quickly gained a wide following due to its ease of implementation and broad applicability. In this minisymposium, we present exciting new extensions and applications of DMD. These include theoretical advances in rigorously defining DMD and its connections to Koopman operator theory, as well as applications in fluid mechanics, neuroscience, and epidemiology. We also introduce algorithmic enhancements that account for the effects of control inputs, correct for noise, and enable ever-larger computations, for instance using compressive sensing.

Organizer: Jonathan H. TuUniversity of California, Berkeley, USA

Organizer: Steven BruntonUniversity of Washington, USA

1:15-1:40 A Rigorous Definition and Theory of Dynamic Mode DecompositionJonathan H. Tu, University of California,

Berkeley, USA; Clarence Rowley, Princeton University, USA

1:45-2:10 On the Relationship Between Koopman Mode Decomposition and Dynamic Mode DecompositionHassan Arbabi and Igor Mezic, University

of California, Santa Barbara, USA

2:15-2:40 Dynamic Mode Decomposition with Control with a Special Focus on Epidemiological ApplicationsJoshua L. Proctor, Intellectual Ventures,

USA

2:45-3:10 Extracting Spatial-Temporal Coherent Patterns in Large-Scale Neural Recordings Using Dynamic Mode DecompositionBing W. Brunton, University of

Washington, USA

2:15-2:40 Hierarchical Subsystem Clustering for Distributed Control of Networked SystemsTomonori Sadamoto, Takayuki Ishizaki,

and Jun-ichi Imura, Tokyo Institute of Technology, Japan

2:45-3:10 Stability of Power Grid: Dynamical Systems PerspectiveAndrej Gajduk, Macedonian Academy of

Sciences and Arts, Macedonia; Mirko Todorovski, Saints Cyril and Methodius University of Skopje, Macedonia; Lasko Basnarkov, Macedonian Academy of Sciences and Arts, Macedonia; Ljupco Kocarev, University of California, San Diego, USA


Monday, May 18

CP15Topics in Noisy/Stochastic/Random Dynamical Systems3:45 PM-5:45 PMRoom:Ballroom II

Chair: Kevin Lin, University of Arizona, USA

3:45-4:00 Embedology for Control and Random Dynamical SystemsBoumediene Hamzi, Imperial College

London, United Kingdom; Jake Bouvrie, Massachusetts Institute of Technology, USA

4:05-4:20 Noise Shaping and Pattern Discrimination in Recurrent Spiking Neuronal NetworksHermann Riecke, Tom Zhao, and Siu Fai

Chow, Northwestern University, USA

4:25-4:40 Faster Sensitivity Estimates for Stochastic Differential EquationsKevin K. Lin, University of Arizona, USA;

Jonathan C. Mattingly, Duke University, USA

4:45-5:00 Zero Density of Open Paths in the Lorentz Mirror Model for Arbitrary Mirror ProbabilityDavid P. Sanders, National University

of Mexico, Mexico; Atahualpa Kraemer, Heinrich-Heine Universitaet Duesseldorf, Germany

5:05-5:20 Power System Stochastic ModelingMathew Titus, Yue Zhang, and Eduardo

Cotilla-Sanchez, Oregon State University, USA

5:25-5:40 Noisy-Bar ProblemKorana Burke, University of California,

Davis, USA

Monday, May 18

CP14Topics in Fluids3:45 PM-4:45 PMRoom:Ballroom I

Chair: Robert E. Ecke, Los Alamos National Laboratory, USA

3:45-4:00 Reduced Modeling of Exact Coherent States in Shear FlowCedric Beaume, Imperial College London,

United Kingdom; Greg Chini, University of New Hampshire, USA; Keith Julien, University of Colorado Boulder, USA; Edgar Knobloch, University of California, Berkeley, USA

4:05-4:20 Effects of Fluid Dynamics on Experiments with Compressed/ Expanded Surfactant MonolayersMaria Higuera, Jose Perales, and Jose

Vega, Universidad Politécnica de Madrid, Spain

4:25-4:40 Stratified Shear Turbulence ExperimentsRobert E. Ecke, Los Alamos National

Laboratory, USA; Philippe Odier, ENS Lyon, France

Monday, May 18

MS44Recent Advances in Ergodic Theory with an Eye to Applications1:15 PM-3:15 PMRoom:Primrose B

Many modelling approaches in applied dynamical systems rely either directly, or indirectly on theoretical results from ergodic theory. Ergodic theory can provide a framework for the modelling process by guiding us to make productive simplifications to the model and/or can suggest directions in which to study a given model (e.g. invariants, exponents, correlations, and their rates of decay, almost invariant states and so-on) or more directly, through numerical implementation of theoretical results, either in an experimental or a rigorous context. This minisymposium will provide a sample from the range of recent contributions to applications and theoretical advances in the field, the latter, ‘with an eye to applications’.

Organizer: Chris BoseUniversity of Victoria, Canada

1:15-1:40 Rigorous Numerical Approximation of Invariant Measures -- History and Recent ProgressChris Bose, University of Victoria, Canada

1:45-2:10 A Measurable Perspective on Finite Time CoherenceErik Bollt and Tian Ma, Clarkson

University, USA

2:15-2:40 Non-Autonomous Dynamical Systems, Multiplicative Ergodic Theorems and ApplicationsCecilia Gonzalez Tokman and Gary

Froyland, University of New South Wales, Australia; Anthony Quas, University of Victoria, Canada

2:45-3:10 On Triangularization of Matrix Cocycles in the Multiplicative Ergodic TheoremJoseph Horan, University of Victoria,

Canada



Monday, May 18

CP18Topics in Complex Systems3:45 PM-5:45 PMRoom:Magpie B

Chair: Steven H. Strogatz, Cornell University, USA

3:45-4:00 Dynamics of Correlated NoveltiesSteven H. Strogatz, Cornell University,

USA

4:05-4:20 Hysteresis Effects in Pedestrian FlowsPoul G. Hjorth and Jens Starke, Technical

University of Denmark, Denmark

4:25-4:40 Robustness of Nonlinear ModelsFabio Della Rossa, Alessandro Colombo,

Fabio Dercole, and Carlo Piccardi, Politecnico di Milano, Italy

4:45-5:00 Systems with Hidden Slow Fast DynamicsPeter Szmolyan, Vienna University of

Technology, Austria

5:05-5:20 A New Filter for State Estimation in Neural Mass ModelsDean R. Freestone, University of

Melbourne, Melbourne, Australia & Columbia University, New York, USA; Philippa Karoly, Dragan Nesic, Mark Cook, and David Grayden, University of Melbourne, Australia

5:25-5:40 Inferring Causal Structures in Complex Systems Via Causation EntropyCarlo Cafaro, Warren Lord, Jie Sun, and

Erik Bollt, Clarkson University, USA

Monday, May 18

CP17Topics in Computational Dynamical Systems II3:45 PM-5:45 PMRoom:Magpie A

Chair: James D. Meiss, University of Colorado Boulder, USA

3:45-4:00 The Existence of Horseshoe Dynamics in Three Dimensional Lotka-Volterra SystemsRizgar Salih and Colin Christopher,

Plymouth University, United Kingdom

4:05-4:20 Invariant Manifolds and Space Mission Design in the Restricted Four-Body ProblemKaori Onozaki and Hiroaki Yoshimura,

Waseda University, Japan

4:25-4:40 Efficient Kernel Algorithm for the Dynamic Mode Decomposition of Observed DataWataru Kurebayashi, Sho Shirasaka,

and Hiroya Nakao, Tokyo Institute of Technology, Japan

4:45-5:00 Perturbing the Cat Map: Mixed Elliptic and Hyperbolic DynamicsJames D. Meiss, University of Colorado

Boulder, USA; Lev Lerman, Lobachevsky State University of Nizhny Novgorod, Russia

5:05-5:20 Classification of Critical Sets and Images for Quadratic Maps of the PlaneBruce B. Peckham, University of

Minnesota, Duluth, USA; Chia-Hsing Nien, Providence University, Taiwan; Richard McGehee, University of Minnesota, Duluth, USA; Bernd Krauskopf and Hinke M. Osinga, University of Auckland, New Zealand

5:25-5:40 Mixing on a HemispherePaul Park, Paul Umbanhowar, Julio Ottino,

and Richard M. Lueptow, Northwestern University, USA

Monday, May 18

CP16Topics in Networks II3:45 PM-5:25 PMRoom:Ballroom III

Chair: Renate A. Wackerbauer, University of Alaska, Fairbanks, USA

3:45-4:00 Control of Stochastic and Induced Switching in Biophysical Complex NetworksDaniel Wells, William Kath, and Adilson E.

Motter, Northwestern University, USA

4:05-4:20 Effects of Network Structure on the Synchronization of Hamiltonian SystemsYogesh Virkar, Juan G. Restrepo, and

James D. Meiss, University of Colorado Boulder, USA

4:25-4:40 Transient Spatiotemporal Chaos in a Network of Coupled Morris-Lecar NeuronsRenate A. Wackerbauer and Jacopo

Lafranceschina, University of Alaska, Fairbanks, USA

4:45-5:00 Studies of Stable Manifolds of a Spatially Extended Lattice Kuramoto ModelAndrea J. Welsh and Flavio Fenton,


5:05-5:20 Consequence of Symmetry Breaking in Two Coupled Kuramoto NetworksScott T. Watson, Ernest Barreto, Bernard

Cotton, and Paul So, George Mason University, USA


Monday, May 18

CP21Topics in Biological Dynamics III3:45 PM-5:25 PMRoom:Maybird

Chair: Vladimir E. Bondarenko, Georgia State University, USA

3:45-4:00 A Model of Heart Rate Dynamics for Changes in Exercise IntensityMichael J. Mazzoleni, Duke University,

USA; Claudio Battaglini, University of North Carolina at Chapel Hill, USA; Brian Mann, Duke University, USA

4:05-4:20 The Evolutionary Dynamics of Gamete Recognition GenesDavid Mcavity and Mottet Geneva,

Evergreen State College, USA

4:25-4:40 Β-Adrenergic Regulation of Action Potential and Calcium Dynamics in a Model of Mouse Ventricular MyocytesVladimir E. Bondarenko, Georgia State

University, USA

4:45-5:00 Spike Time Dependent Plasticity in a Spiking Neural NetworkAnushaya Mohapatra, Oregon State

University, USA; Mike Field and Chris Bick, Rice University, USA

5:05-5:20 A Mathematical Model for Frog Population Dynamics with Batrachochydrium Dendrobatidis (Bd) InfectionBaoling Ma, University of Louisiana,

Lafayette, USA

Monday, May 18

CP20Topics in Computational Dynamical Systems & Pattern Formation3:45 PM-5:25 PMRoom:Wasatch B

Chair: Mikheil Tutberidze, Ilia State University, Georgia

3:45-4:00 Nonlinear Behaviors As Well As Bifurcation Mechanism in Switched Dynamical SystemsYu V. Wang, City College of New York,

USA

4:05-4:20 Gpu-Based Computational Studies of the Interaction Between Reentry Waves and Gap Junctional Uncoupling in Cardiac TissuesZhihui Zhang, Florida State University,

USA

4:25-4:40 On the Numerical Integration of One Nonlinear Parabolic EquationMikheil Tutberidze, Ilia State University,

Georgia

4:45-5:00 A Continuous Model for the Pathfinding Problem with Self-Recovery PropertyKei-Ichi Ueda, University of Toyama,

Japan; Masaaki Yadome and Yasumasa Nishiura, Tohoku University, Japan

5:05-5:20 Patterns on Curved Backgrounds: the Influence of Local Curvature on Pattern FormationFrits Veerman and Philip K. Maini,

University of Oxford, United Kingdom

Monday, May 18

CP19Topics in Classical Dynamical Systems3:45 PM-5:45 PMRoom:Wasatch A

Chair: Kelum D. Gajamannage, Clarkson University, USA

3:45-4:00 New Asymptotics of Homoclinic Orbits Near Bogdanov-Takens Bifurcation PointBashir M. Al-Hdaibat and Willy

Govaerts, Ghent University, Belgium; Yuri Kuznetsov, University of Twente, Netherlands; Hil Meijer, Twente University, Netherlands

4:05-4:20 Metric Invariance Entropy and Conditionally Invariant MeasuresFritz Colonius, University of Augsburg,

Germany

4:25-4:40 Periodic Orbit Theory of Continuous MediaNazmi Burak Budanur and Predrag

Cvitanovic, Georgia Institute of Technology, USA

4:45-5:00 A Dynamical and Algebraic Study of a Family of Lienard Equations Transformable to Riccati EquationsPrimitivo B. Acosta-Humanez, Jorge

Rodriguez-Contreras, and Alberto Reyes-Linero, Universidad del Atlantico, Colombia

5:05-5:20 Dimensionality Reduction of Collective Motion by Principal ManifoldsKelum D. Gajamannage, Clarkson

University, USA; Sachit Butail, Indraprastha Institute of Information Technology Delhi, India; Maurizio Porfiri, Polytechnic Institute of New York University, USA; Erik Bollt, Clarkson University, USA

5:25-5:40 A Fast Explicit Method for Computing Invariant Solutions of High-Dimensional Dynamical Systems with Continuous SymmetriesMohammad Farazmand and Predrag

Cvitanovic, Georgia Institute of Technology, USA


Monday, May 18

CP24Topics in Wave Dynamics3:45 PM-5:25 PMRoom:Primrose A

Chair: Ibrahim Fatkullin, University of Arizona, USA

3:45-4:00 Coupled Parametrically Forced Oscillators and Modulated Cross-WavesJeff Porter, Pablo Salgado Sanchez, Ignacio

Tinao, and Ana Laveron-Simavilla, Universidad Politécnica de Madrid, Spain

4:05-4:20 Finding the Stokes Wave: From Low Steepness to Almost Limiting WaveSergey Dyachenko, University of Arizona,

USA

4:25-4:40 Singularities of the Stokes’ Wave: Numerical SimulationAlexander O. Korotkevich, University of

New Mexico, USA

4:45-5:00 Branch Cut Singularity of Stokes WavePavel M. Lushnikov, University of New

Mexico, USA

5:05-5:20 Blow-Ups in Nonlinear Pdes, Composite Grid-Particle Methods, and Stochastic Particle SystemsIbrahim Fatkullin, University of Arizona,

USA

Monday, May 18

CP23Topics in Optical and Related Systems3:45 PM-5:45 PMRoom:Superior B

Chair: Estathios Charalampidis, University of Massachusetts, USA

3:45-4:00 Control of Extreme Events in the Bubbling Onset of Wave Turbulence in the Forced and Damped Non-Linear Schrödinger EquationPaulo Galuzio, Ricardo L. Viana, and

Sergio R. Lopes, Federal University of Paraná, Brazil

4:05-4:20 Vector Rogue Waves and Dark-Bright Boomeronic Solitons in Autonomous and Non-Autonomous SettingsEfstathios Charalampidis, University

of Massachusetts, Amherst, USA; R. BABU Mareeswaran and T. Kanna, Bishop Heber College, India; Panayotis Kevrekidis, University of Massachusetts, USA; Dimitri Frantzeskakis, University of Athens, Greece

4:25-4:40 Reducibility of One-dimensional Quasi-periodic Schrödinger EquationsJiansheng Geng, Nanjing University, China

4:45-5:00 Numerical Continuation of Invariant Solutions of the Complex Ginzburg-Landau EquationVanessa Lopez, IBM T.J. Watson Research

Center, USA

5:05-5:20 Nonlinear Oscillations and Bifurcations in Silicon Photonic ResonatorsAlexander Slawik and Daniel Abrams,


5:25-5:40 Noise and Determinism of Stimulated Brillouin Scattering Dynamics in Optical FiberDiana A. Arroyo-Almanza, Rafael Setra,

and Zetian Ni, University of Maryland, USA; Thomas E. Murphy, University of Maryland, College Park, USA; Rajarshi Roy, University of Maryland, USA

Monday, May 18

CP22Delay Dynamical Systems & Time Series Analysis3:45 PM-5:05 PMRoom:Superior A

Chair: Sue Ann Campbell, University of Waterloo, Canada

3:45-4:00 Plankton Models with Time DelaySue Ann Campbell, Matt Kloosterman, and

Francis Poulin, University of Waterloo, Canada

4:05-4:20 Stochastic Delay in Gene Regulation: Exact Stability AnalysisMehdi Sadeghpour and Gabor Orosz,

University of Michigan, Ann Arbor, USA

4:25-4:40 Computational Topology Techniques for Characterizing Time Series DataElizabeth Bradley, James D. Meiss, and

Joshua T. Garland, University of Colorado Boulder, USA; Nicole Sanderson, University of Colorado, USA

4:45-5:00 Noise, Chaos and Entropy Generation in a Time-Delayed Dynamical SystemAaron M. Hagerstrom and Rajarshi Roy,

University of Maryland, USA; Thomas E. Murphy, University of Maryland, College Park, USA


Monday, May 18

PD1Journal Editors Panel and Reception (pizza and light refreshments available)7:00 PM-8:00 PMRoom:Ballroom

Chair: Lora Billings, Montclair State University, USA

Wondering where to submit your next manuscript? What is the optimal journal for publishing work? How does the editorial process work? In this panel, editors of the leading journals in the area of dynamical systems will be making short presentations to inform potential authors and readers. Editors will describe the subject areas covered by their journals, describe their acceptance criteria and the editorial process they use to evaluate manuscripts, and will also present vital statistics for their journals. As a collection, journals in the field span a broad spectrum with a tremendous variation in authors, audiences, traditions, and editorial practices. One goal of this panel, a first of its kind, is to scope the publication landscape in dynamical systems. The presentations will be followed by a reception sponsored by the publishing companies. In this informal setting, editors will be available answer questions. Pizza and light refreshments will be served.

Panelists:Eli Ben-NaimLos Alamos National Laboratory, USA -

Physical Review E, American Physical Society

David CampbellBoston University, USA - Chaos, American

Institute of Physics

Serena DalenaPhysical Review Letters, American Physical

Society, USA

Charles DoeringUniversity of Michigan, USA - Physics

Letters A, Elsevier

Edgar KnoblochUniversity of California, Berkeley, USA -

Nonlinearity, Institute of Physics

Joceline LegaUniversity of Arizona, USA - Physica D,

Elsevier

Bjorn SandstedeBrown University, USA - SIAM Journal on

Applied Dynamical Systems (SIADS)

Monday, May 18

IP3Filtering Partially Observed Chaotic Deterministic Dynamical Systems6:00 PM-6:45 PMRoom:Ballroom

Chair: Bjorn Sandstede, Brown University, USA

This talk is concerned with determining the state of a chaotic dynamical system, for which the initial condition is only known probabilisticlly, given partial and noisy observations. In particular it is of interest to study this problem in the limit of a large number of such observations, over a long time interval. A key question is to determine which observations are sufficient in order to accurately recover the signal, and thereby overcome the lack of predictability caused by sensitive dependence on initial conditions. A canonical application is the development of probabilistic weather forecasts. In order to study this problem concretely, we will focus on a wide class of dissipative differential equations with quadratic energy-conserving nonlinearity, including the Navier-Stokes equation on a two dimensional torus. The work presented is contained in the paper D. Sanz-Alonso and A.M.Stuart, “Long-time asymptotics of the filtering distribution for partially observed chaotic deterministic dynamical systems” (http://arxiv.org/abs/1411.6510); see also the paper K.J.H. Law, A. Shukla and A.M. Stuart, “Analysis of the 3DVAR filter for the partially observed Lorenz ‘63 model,’” Discrete and Continuous Dynamical Systems A, 34(2014), and the book K.J.H. Law, A.M.Stuart and K. Zygalalkis, “Data Assimilation: A Mathematical Introduction” (in preparation, 2015) for further background references.

Andrew StuartUniversity of Warwick, United Kingdom

Intermission6:45 PM-7:00 PM

Monday, May 18

CP25Topics in Classical and Fluid Dynamical Systems3:45 PM-5:25 PMRoom:Primrose B

Chair: To Be Determined

3:45-4:00 Experiments on a Pinball-Like OscillatorLawrie N. Virgin, Duke University, USA

4:05-4:20 Jetting-BubblingTransition in MicroflowsDipin S. Pillai and S. Pushpavanam, Indian

Institute of Technology Madras, India

4:25-4:40 Exploring the Hyperbolicity of Chaotic Rayleigh-Bénard ConvectionMu Xu and Mark Paul, Virginia Tech, USA

4:45-5:00 Snakes on An Invariant Plane: Coupled Translational-Rotational Dynamics of Flying SnakesIsaac Yeaton, Hodjat Pendar, Jake Socha,

and Shane D. Ross, Virginia Tech, USA

5:05-5:20 Finding Model Parameters Without Prior Knowledge of Solve-Able Regions: A Solar Thermochemistry Case-StudyKarl Schmitt, Luke Venstrom, William D.

Arloff, and Leandro Jaime, Valparaiso University, USA

Intermission5:45 PM-6:00 PM


Tuesday, May 19

MS45Energy Transfer and Harvesting in Nonlinear Systems - Part II of II8:30 AM-10:30 AMRoom:Ballroom I

For Part 1 see MS32 The minisymposium will focus on recent developments and challenges related to energy transfer and harvesting in nonlinear systems. Special attention will be paid to rapidly developing research field of nonsmooth systems. Topics will include, but will not be limited to:

• New results in the classical problem of divergent vs convergent heat conduction in models of atomic lattices;

• Description of wave initiation, propagation and mitigation in granular systems;

• Nonlinear targeted energy transfer in systems with strongly nonlinear attachments

• Applications of strong and non-smooth nonlinearities for efficient energy harvesting.

Organizer: Oleg Gendelman

Technion Israel Institute of Technology, Israel

Organizer: Alexander VakakisUniversity of Illinois, USA

8:30-8:55 Non-Linearizable Wave Equation: Nonlinear Sonic VacuumLeonid Manevich, Russian Academy of

Sciences, Russia; Alexander Vakakis, University of Illinois, USA

9:00-9:25 Vibration Energy Harvesting Based on Nonlinear Targeted Energy TransferKevin Remick, University of Illinois at

Urbana-Champaign, USA; D Dane Quinn, University of Akron, USA; D. Michael McFarland, University of Illinois, USA; Lawrence Bergman, University of Illinois at Urbana-Champaign, USA; Alexander Vakakis, University of Illinois, USA

9:30-9:55 Nonlinear Energy Harvesting in Granular MediaChristopher Chong, ETH Zürich, Switzerland

10:00-10:25 2D Energy Channeling in the Locally Resonant Acoustic MetamaterialsYuli Starosvetsky and Kirill Vorotnikov,

Technion - Israel Institute of Technology, Israel

Tuesday, May 19


Monday, May 18SIAG/DS Business Meeting8:30 PM-9:30 PMRoom:Ballroom

Complimentary wine and beer will be served.


Tuesday, May 19

MS48Bridging the Gap Between Observations and Idealized Modeling: A Comprehensive Approach to Weather and Climate Predictability8:30 AM-10:30 AMRoom:Magpie A

Many important climate and weather phenomenon are difficult to predict because of abrupt transitions in behavior due to noise and nonlinearity. Determining whether noise and nonlinearity manifest themselves as an organizing or random forcing has important consequences for model choice and subsequent mechanistic understanding and predictability. This minisymposium is centered on a two-fold approach to addressing this issue. First, observational data is used as a tool to identify the relevant physical processes that are at the core of complex atmospheric systems. Second, the insights gained from observations are leveraged to create simple, but physically unabridged representations of real-world atmospheric phenomenon.

Organizer: Juliana DiasNOAA Earth System Research Laboratory

8:30-8:55 An Observational Basis for Sudden Stratospheric Warmings As Bifurcations in Planetary Wave AmplitudeJohn R. Albers, University of Colorado,

USA

9:00-9:25 The Role of Noise in Bifurcations in Fluids and the AtmosphereYuzuru Sato, Hokkaido University, Japan;

David J. Albers, Columbia University, USA

9:30-9:55 Tropical-Extratropical Wave Interactions in the AtmosphereJuliana Dias, NOAA Earth System

Research Laboratory

10:00-10:25 The Use of Green Functions of the Shallow Water Model for Understanding Climate AnomaliesPedro Leite da Silva Dias, University of

Sao Paulo, Brazil

Tuesday, May 19

MS47Koopman Operator Techniques in Dynamical Systems: Theory and Practice - Part I of II8:30 AM-10:30 AMRoom:Ballroom III

For Part 2 see MS60 Koopman operator is a linear infinite-dimensional composition operator that can be defined for arbitrary nonlinear dynamical systems. It retains the full information of the nonlinear state-space dynamics. Study of its spectral properties provides an alternate framework for dynamical systems analysis. Recently, the spectral theory of Koopman operator has been extended to dissipative systems. This enabled numerous applications based on the so-called Koopman Mode Expansion in fields as diverse as fluid mechanics, image processing and power grid engineering. In this minisymposium, we aim to present and discuss the current status of Koopman operator techniques in theory and practice of dynamical systems.

Organizer: Igor MezicUniversity of California, Santa Barbara, USA

Organizer: Yoshihiko SusukiKyoto University, Japan

8:30-8:55 Koopman Mode Expansion in Theory and PracticeIgor Mezic, University of California, Santa

Barbara, USA

9:00-9:25 What Can the Koopman Operator Do for Dynamical Systems?Rainer Nagel, University of Tübingen,

Germany

9:30-9:55 Generalized Laplace Analysis and Spaces of Observables for the Koopman OperatorRyan Mohr, University of California, Santa

Barbara, USA

10:00-10:25 Computation of the Koopman Eigenfunctions Is a Systematic Method for Global Stability AnalysisAlexandre Mauroy, University of Liege,

Belgium; Igor Mezic, University of California, Santa Barbara, USA

Tuesday, May 19

MS46Cellular Decision Making Under Noise8:30 AM-10:30 AMRoom:Ballroom II

Understanding how living cells make decisions based on environmental inputs is one of the keys to understanding all living systems. In the past decade, the behavior of genetic circuits has been studied in great detail, both theoretically and experimentally. While most studies focused on the role of intrinsic noise, extrinsic noise has remained largely unexplored, even though it may dramatically affect the behavior of these systems. Understanding the combined influence of intrinsic and extrinsic noise on the stochastic dynamics of gene expression should give us insight on how biochemical networks have evolved to both control and exploit their fluctuating environment.

Organizer: Michael AssafHebrew University of Jerusalem, Israel

8:30-8:55 The Effect of Extrinsic Noise on Gene RegulationMichael Assaf, Hebrew University of

Jerusalem, Israel

9:00-9:25 Fundamental Limits to the Precision of Multicellular SensingAndrew Mugler, Purdue University,

USA; Matthew Brennan, Johns Hopkins University, USA; Andre Levchenko, Yale University, USA; Ilya Nemenman, Emory University, USA

9:30-9:55 Inferring Predictive Signal-Activated Gene Regulation Models from Noisy Single-Cell DataBrian Munsky, Colorado State University,

USA

10:00-10:25 Coarse-Graining Biochemical NetworksNikolai Sinitsyn, Los Alamos National

Laboratory, USA


Tuesday, May 19

MS51Mechanisms for Computations in Neuronal Networks8:30 AM-10:30 AMRoom:Wasatch B

Our speakers address a range of neural network mechanisms in order to understand their impact on specific computations, including: synchrony detection through phase-delayed inhibition, olfactory coding using time-varying oscillations, and transfer of correlations through convergent network motifs.

Organizer: Andrea K. BarreiroSouthern Methodist University, USA

Organizer: Pamela B. FullerRensselaer Polytechnic Institute, USA

8:30-8:55 Impact of Single-Neuron Dynamics on Transfer of Correlations from Common InputAndrea K. Barreiro, Southern Methodist

University, USA

9:00-9:25 Integrate-and-Fire Model of Insect OlfactionPamela B. Fuller and Gregor Kovacic,

Rensselaer Polytechnic Institute, USA; David Cai, Shanghai Jiao Tong University, China and Courant Institute of Mathematical Sciences, New York University, USA

9:30-9:55 A Network of Excitatory and Inhibitory Neurons with Gap JunctionsJennifer Kile and Gregor Kovacic,

Rensselaer Polytechnic Institute, USA; David Cai, Shanghai Jiao Tong University, China and Courant Institute of Mathematical Sciences, New York University, USA

10:00-10:25 Phase Delayed Inhibition and the Representation of Whisker Deflection Velocity in the Rodent Barrel CortexMainak Patel, College of William & Mary,

USA; Runjing Liu, Duke University, USA; Badal Joshi, California State University, San Marcos, USA

Tuesday, May 19

MS50Multistability in Biological Circuits: Theory and Applications8:30 AM-10:00 AMRoom:Wasatch A

Complex networks facilitate the existence of multiple coexisting stable states in the network dynamics. This is most prominent in biological, gene, and neural networks that derive their functional flexibility from a high multiplicity of operational modes. Robustness and multiplicity as well as the transition dynamics is determined by network symmetry, structure and node dynamics. The struggle of understanding such complex network dynamics has inspired novel mathematical approaches and continues to uncover fascinating mechanisms of real network function. The speakers in this session will present novel mathematical problems of understanding dynamical transitions on complex biological networks.

Organizer: Marcos RodriguezCentro Universitario De La Defensa Zaragoza, Spain

Organizer: Justus T. SchwabedalGeorgia State University, USA

8:30-8:55 From Andronov-Hopf to Z_3 Heteroclinic Bifurcations in CpgsMarcos Rodriguez, Centro Universitario

De La Defensa Zaragoza, Spain; Roberto Barrio and Sergio Serrano, University of Zaragoza, Spain; Andrey Shilnikov, Georgia State University, USA

9:00-9:25 Intrinsic Mechanisms for Pattern Generation in Three-Node NetworksJarod Collens, Aaron Kelley, Deniz Alacam,

Tingli Xing, Drake Knapper, Justus T. Schwabedal, and Andrey Shilnikov, Georgia State University, USA

9:30-9:55 Key Bifurcations of Bursting Polyrhythms in 3-Cell Central Pattern GeneratorsJeremy Wojcik, Applied Technology

Associates, USA; Robert Clewley, Justus T. Schwabedal, and Andrey Shilnikov, Georgia State University, USA

Tuesday, May 19

MS49Theory and Applications of Nonsmooth Dynamics in Physical Systems - Part II of II8:30 AM-10:00 AMRoom:Magpie B

For Part 1 see MS36 This minisymposium will provide a mix of talks featuring theoretical developments in nonsmooth systems as well as talks featuring applications with nonsmooth dynamics. In either case, physical applications provide the motivation for mathematical exploration. Additionally, the minisymposium will blend talks appropriate for a broad audiences and talks geared at experts. To that point, the minisymposium will begin with the very general “How nonsmooth are the Earth sciences?” which will set the stage for the rest of the speakers. Other talks will discuss issues such as generalized bifurcations, canard phenomena, synchronization, and the new area of resilience.

Organizer: Andrew RobertsCornell University, USA

Organizer: Esther WidiasihUniversity of Hawaii, West Oahu, USA

8:30-8:55 Canard Phenomena in Nonsmooth SystemsAndrew Roberts, Cornell University, USA

9:00-9:25 Generalized Hopf Bifurcation in a Nonsmooth Climte ModelJulie Leifeld, University of Minnesota,

USA

9:30-9:55 Dangerous Border Collision Bifurcation in Piecewise Smooth MapsSoumitro Banerjee and Arindam Saha,

Indian Institute for Science Education and Research, Kolkata, India; Viktor Avrutin, University of Stuttgart, Germany; Laura Gardini, University of Urbino, Italy


Tuesday, May 19

MS54Renewable Energy and Power Grids: Their Mathematical Characterizations - Part II of II8:30 AM-10:00 AMRoom:Superior B

For Part 1 see MS41 It is our social demand to introduce more renewable energy resources into power grids. However, because renewable energy outputs fluctuate according to weather conditions, we need to control and/or optimize power grids so that we can keep the voltage and frequency as constant and stable. Here we put together some recent advances to achieve this need mathematically. This need for more renewables makes us to combine several fields of mathematics together such as dynamical systems theory, control theory and complex network theory. This need also brings us into new research directions, which will turn our mathematical tools more practical.

Organizer: Yoshito HirataUniversity of Tokyo, Japan

Organizer: Jun-ichi ImuraTokyo Institute of Technology, Japan

Organizer: Juergen KurthsPotsdam Institute for Climate Impact Research and Humboldt University Berlin, Germany

8:30-8:55 Basin Stability for Evaluating Large Perturbations in Power GridsJuergen Kurths, Potsdam Institute for

Climate Impact Research and Humboldt University Berlin, Germany

9:00-9:25 Model Free Tuning of Wind Farms for Maximizing Power ProductionMohd Ashraf Ahmad, Shun-Ichi Azuma,

and Toshiharu Sugie, Kyoto University, Japan

9:30-9:55 Predicting Critical Links in Complex Supply NetworksMarc Timme, Max-Planck-Institute for

Dynamics and Self-Organization, Germany; Dirk Witthaut, Forschungszentrum Jülich, Germany; Martin Rohden, University of Bremen, Germany; Xiaozhu Zhang and Sarah Hallerberg, Max Planck Institute for Dynamics and Self-Organization, Germany

Tuesday, May 19

MS53Ostwald Ripening, Aggregate Growth and Precipitation8:30 AM-10:30 AMRoom:Superior A

The minisymposium will address new developments on the impact of fluctuations of the environment on aggregate growth and the emergence of precipitation. There will comprise two times two talks. There will be two talks addressing recent theoretical progress focusing on Ostwald ripening and the crossover to a runaway growth leading to precipitation, respectively. Another two talks, will address recent advances in applications, nanoparticle synthesis and steel production.

Organizer: Jürgen VollmerMax Planck Institute for Dynamics and Self-Organization, Germany

8:30-8:55 Episodic PrecipitatonJürgen Vollmer, Max Planck Institute


9:00-9:25 Ostwald Ripening and Nanoparticle GrowthMartin Rohloff, Max Planck Institute


9:30-9:55 Aggregate Growth in Optimizing Steel ProductionNikolas Rimbert, Université de Lorraine,

France

10:00-10:25 Initiation of Rain and Inertial ParticlesMarkus Abel, University of Potsdam,

Germany

Tuesday, May 19

MS52Reduced Dynamical Models and Their Applications - Part II of II8:30 AM-10:30 AMRoom:Maybird

For Part 1 see MS39 The purpose is to present a cross-section of leading-edge research on the development, analysis, numerical solution, visualization and applications of reduced dynamical systems models. These models may arise via simplification of form of infinite-dimensional systems, reduction in cardinality of the dimension, possibly by restriction to invariant submanifolds, and ad hoc techniques based upon focusing on certain combinations of variables. Among the reductions to be discussed are simplified infinite-dimensional models for granular flows, reduced dimensional models via extensions of the zero derivative principle, discrete dynamical systems reductions for logical circuits and ecological models, and discrete integrable reductions of continuum models.

Organizer: Denis BlackmoreNew Jersey Institute of Technology, USA

Organizer: Anthony RosatoNew Jersey Institute of Technology, USA

8:30-8:55 Idealized Models for Vortex Shedding and Fluid-Body InteractionsScott D. Kelly, University of Illinois at

Urbana-Champaign, USA

9:00-9:25 A Novel Semidiscete Scheme for a Reduced Continuum Flow ModelHao Wu and Denis Blackmore, New Jersey

Institute of Technology, USA

9:30-9:55 Visualization of Reduced Granular DynamicsXavier M. Tricoche, Purdue University,

USA

10:00-10:25 Extending the Zero Derivative PrincipleMorten Brons, Technical University

of Denmark, Denmark; Eric Benoît, Universitè de la Rochelle, France; Mathieu Desroches and Maciej Krupa, INRIA Paris-Rocquencourt, France


Tuesday, May 19

MS57Chaos and Strange Attractors8:30 AM-10:30 AMRoom:Primrose B

The purpose of this minisymposium is to discuss the state of the art in the modern chaos theory and applications of the theory to problems in biology, chemistry, mechanics etc.

Organizer: Ivan OvsyannikovUniversity of Bremen, Germany

8:30-8:55 Global Invariant Manifolds Unravelling Shilnikov ChaosPablo Aguirre, Universidad Técnica

Federico Santa María, Chile; Bernd Krauskopf and Hinke M. Osinga, University of Auckland, New Zealand

9:00-9:25 Analytic Proof of Lorenz Attractors in Flows and MapsIvan Ovsyannikov, University of Bremen,

Germany

9:30-9:55 The Lorenz System Near the Loss of the Foliation ConditionJennifer L. Creaser, Bernd Krauskopf, and

Hinke M. Osinga, University of Auckland, New Zealand

10:00-10:25 The Many Facets of ChaosEvelyn Sander, George Mason University,

USA


Tuesday, May 19

MS56Topology and Computation in Dynamics8:30 AM-10:30 AMRoom:Primrose A

Classical Morse theory provides a direct link between the topology of a manifold and gradient dynamics on it. Extensions of Morse-theoretic ideas due to Conley (in the finite dimensional setting) and Floer (in the infinite dimensional cases) are powerful topological tools in applied dynamical systems. In particular, the associated homology provides computable invariants of dynamical systems. This homology is thus well-suited for numerical approaches to understanding global dynamics. This minisymposium explores recent advances in finite and infinite dimensional dynamical systems using Morse-Conley-Floer index techniques, rigorous computational dynamics, ‘database’ explorations based on Conley-Morse graphs, and topological reconstruction from data.

Organizer: Jan Bouwe Van Den BergVU University, Amsterdam, Netherlands

Organizer: Robert VandervorstVU University, Amsterdam, Netherlands

8:30-8:55 Rigorous Computing in Strongly Indefinite ProblemsJean-Philippe Lessard, Université Laval,

Canada; Jan Bouwe Van Den Berg and Robert Vandervorst, VU University, Amsterdam, Netherlands; Marcio Gameiro, University of Sao Paulo, Brazil

9:00-9:25 Computing Conley-Morse DatabasesShaun Harker, Rutgers University, USA

9:30-9:55 Reconstructing Functions from Dense SamplesVidit Nanda, University of Pennsylvania,

USA

10:00-10:25 Morse Homology on Spaces of BraidsPatrick Hafkenscheid, VU University,

Amsterdam, Netherlands

Tuesday, May 19

MS55Extensions and Applications of Dynamic Mode Decomposition - Part II of II8:30 AM-10:30 AMRoom:White Pine

For Part 1 see MS42 Dynamic mode decomposition (DMD) is a powerful method that identifies spatial-temporal coherent structures in high-dimensional datasets. Introduced less than a decade ago, it has quickly gained a wide following due to its ease of implementation and broad applicability. In this minisymposium, we present exciting new extensions and applications of DMD. These include theoretical advances in rigorously defining DMD and its connections to Koopman operator theory, as well as applications in fluid mechanics, neuroscience, and epidemiology. We also introduce algorithmic enhancements that account for the effects of control inputs, correct for noise, and enable ever-larger computations, for instance using compressive sensing.

Organizer: Jonathan H. TuUniversity of California, Berkeley, USA

Organizer: Steven BruntonUniversity of Washington, USA

8:30-8:55 Using Dynamic Mode Decomposition to Extract Linear Global Modes from Nonlinear Fluid Flow SolversKunihiko Taira and Aditya Nair, Florida

State University, USA; Shervin Bagheri, KTH Royal Institute of Technology, Sweden

9:00-9:25 Improving the Accuracy of Dynamic Mode Decomposition in the Presence of NoiseScott Dawson, Maziar S. Hemati, Matthew

O. Williams, and Clarence Rowley, Princeton University, USA

9:30-9:55 Parallel Qr Algorithm for Data-Driven Decompositions, in Particular Dynamic Mode DecompositionTaraneh Sayadi, University of Illinois

at Urbana-Champaign, USA; Peter Schmid, Imperial College London, United Kingdom

10:00-10:25 Compressive Sensing and Dynamic Mode DecompositionSteven Brunton, University of Washington,

USA


Tuesday, May 19

MS58Snapshot and Pullback Attractors, a Framework for Understanding Nonautonomous Dissipative Dynamics1:30 PM-3:30 PMRoom:Ballroom I

Snapshot attractors generalize strange attractors from autonomous to nonautonomous dynamics. A snapshot attractor is a time-dependent object in the phase space of an open system that is the asymptotic locus of trajectories initialized in the remote past. Pullback attractors in the deterministic setting and random attractors in the stochastic setting provide a solid mathematical foundation to this loose definition. Random dynamical systems theory encompasses both deterministic and random forcing. The minisymposium will clarify the connections between snapshot and pullback attractors, and shed further light on their invariant measures as generalized SRB measures. Applications will include climate dynamics and coupled oscillators.

Organizer: Michael GhilEcole Normale Superieure de Paris, France, and University of California, Los Angeles, USA

Organizer: Tamas TelEötvös Loránd University, Hungary

1:30-1:55 Random Attractors and How They Help Understand Climate Change and VariabilityMichael Ghil, Ecole Normale Superieure

de Paris, France, and University of California, Los Angeles, USA

2:00-2:25 SRB Measures for Time-Dependent and Random AttractorsLai-Sang Young, Courant Institute of

Mathematical Sciences, New York University, USA

2:30-2:55 Snapshot Attractors and the Transition to Extensive Chaos in Large Systems of Mean-Field Coupled OscillatorsEdward Ott, Wai Lim Ku, and Michelle

Girvan, University of Maryland, USA

Tuesday, May 19

PD2Funding Agency Panel12:00 PM-1:00 PMRoom:Ballroom

Chair: Igor Mezic, University of California, Santa Barbara, USA

A panel of representatives from federal funding agencies will discuss trends and opportunities for research funding in the area of dynamical systems. Each will describe their funding guidelines and deadlines, and provide information about the their particular funding interests.

Panelists:Fariba FahrooAir Force Office of Scientific Research, USA

Predrag NeskovicOffice of Naval Research, USA

Massimo RuzzeneNational Science Foundation, Directorate for

Engineering, USA

Samuel StantonArmy Research Office, USA

Henry WarchallNational Science Foundation, Division of

Mathematical Sciences, USA

Tuesday, May 19

IP4Fields of Dreams: Modeling and Analysis of Large Scale Activity in the Brain11:00 AM-11:45 AMRoom:Ballroom

Chair: Michael Ward, University of British Columbia, Canada

With the advent of optogenetics and the ability to record large numbers of neurons with high temporal resolution, there is now a great deal of interest in both the temporal and spatial activity of neurons in the brain. In this talk, I will discuss a number of old and new developments in the study of these nonlinear integro-differential equations and how they apply to some new biological findings. Topics that I will discuss include the role of noise on spatio-temporal activity, the interaction between extrinsic and intrinsic activity, interactions between multiple spatial networks, and finally some recent applications of Filippov theory to discontinuous neural field models.

Bard ErmentroutUniversity of Pittsburgh, USA




Tuesday, May 19

MS60Koopman Operator Techniques in Dynamical Systems: Theory and Practice - Part II of II1:30 PM-3:30 PMRoom:Ballroom III

For Part 1 see MS47 Koopman operator is a linear infinite-dimensional composition operator that can be defined for arbitrary nonlinear dynamical systems. It retains the full information of the nonlinear state-space dynamics. Study of its spectral properties provides an alternate framework for dynamical systems analysis. Recently, the spectral theory of Koopman operator has been extended to dissipative systems. This enabled numerous applications based on the so-called Koopman Mode Expansion in fields as diverse as fluid mechanics, image processing and power grid engineering. In this minisymposium, we aim to present and discuss the current status of Koopman operator techniques in theory and practice of dynamical systems.

Organizer: Igor MezicUniversity of California, Santa Barbara, USA

Organizer: Yoshihiko SusukiKyoto University, Japan

1:30-1:55 Approximating the Koopman Operator Using Extended Dynamic Mode DecompositionClarence Rowley and Matthew O.

Williams, Princeton University, USA

2:00-2:25 Machine Learning and the Koopman Operator: Algorithms and ApplicationsMatthew O. Williams, Princeton

University, USA

2:30-2:55 Dynamic Mode Decomposition for Multi-Resolution AnalysisJ. Nathan Kutz, University of Washington,

USA

3:00-3:25 Koopman Operator Techniques in Power Grid AnalysisYoshihiko Susuki, Kyoto University, Japan

Tuesday, May 19

MS59Synchronization of Chaos and its Applications - Part I of II1:30 PM-3:30 PMRoom:Ballroom II

For Part 2 see MS72 Many fundamental processes in nature are based on synchronization of chaos. This phenomenon is universal, robust and it may also involve large population of active elements distributed over extensive spatial regions. In this minisymposium theoretical and application issues related to this phenomenon will be considered. In particular, we address the fundamental role that this phenomenon has in the organization of the collective movement, in neuroscience and in the development of scenarios that lead to coexistence of ordered and disordered states.

Organizer: Elbert E. MacauLaboratory for Computing and Applied Mathematics and Brazilian Institute for Space Research, Brazil

Organizer: Epaminondas RosaIllinois State University, USA

1:30-1:55 Chimeras in Networks of Identically Coupled Mechanical OscillatorsRosangela Follmann, Daniel Abrams,

and Adilson E. Motter, Northwestern University, USA

2:00-2:25 Dynamics of Clustering in Networks with Repulsive InteractionMichael A. Zaks, University of Potsdam,

Germany

2:30-2:55 Synchronization Properties Related to Neighborhood Similarity in a Complex Network of Non-Identical OscillatorsElbert E. Macau, Laboratory for

Computing and Applied Mathematics and Brazilian Institute for Space Research, Brazil; Celso Bernardo Freitas, Instituto Nacional de Pesquisas Espaciais, Brazil; Ricardo L. Viana, Federal University of Paraná, Brazil

3:00-3:25 Chimera States in Networks with Symmetry-Breaking CouplingAnna Zakharova, Institute of Theoretical

Physics, Berlin, Germany; Marie Kapeller, Berlin Institute of Technology, Germany; Eckehard Schöll, Technische Universität Berlin, Germany

3:00-3:25 The Quantification of the Nonergodic Property Via Snapshot Attractors: An Application to a Conceptual Climate ModelGabor Drotos, Hungarian Academy

of Sciences, Hungary; Tamas Bodai, Universitat Hamburg, Germany; Tamas Tel, Eötvös Loránd University, Hungary


Tuesday, May 19

MS63Applications of Ensemble Data Assimilation Methods to Climate Processes1:30 PM-3:30 PMRoom:Wasatch A

Data assimilation methods seek to improve estimates from a predictive model by combining them with observed data. Most realistic applications, such as those used in climate modeling, involve an underlying dynamical system which is nonlinear. Many ensemble methods have been designed to handle this nonlinearity, and additionally, often provide an estimate of the uncertainty in the prediction via the ensemble spread. This session will include applications of ensemble data assimilation methods to several aspects of the climate, including oceans, sea ice, and the ionosphere.

Organizer: Laura SlivinskiWoods Hole Oceanographic Institute, USA

1:30-1:55 An Application of Lagrangian Data Assimilation to Katama Bay, MaLaura Slivinski, Larry Pratt, and Irina

Rypina, Woods Hole Oceanographic Institute, USA

2:00-2:25 Ensemble Inflation by Shadowing TechniquesThomas Bellsky, University of Maine,

USA; Lewis Mitchell, University of Adelaide, Australia

2:30-2:55 Ionospheric Weather Forecasting Using the Letkf SchemeJuan Durazo, Arizona State University,

USA

3:00-3:25 Predicting Flow Reversals in a Cfd Simulated Thermosyphon Using Data AssimilationAndrew Reagan, University of Vermont,

USA

Tuesday, May 19

MS62Dynamics of Nanoelectromechanical Systems (NEMS)1:30 PM-3:00 PMRoom:Magpie B

Nanoelectromechanical systems (NEMS) are the latest step in miniaturizing electro-mechanical devices. Due to their scale, we can now study new physical regimes as well as develop novel technologies. The minisymposium presents an overview of their rich nonlinear and pattern formation dynamics alongside new theoretical and experimental advances. The talks will address systems consisting of single NEMS devices as well as NEMS networks.

Organizer: Korana BurkeUniversity of California, Davis, USA

1:30-1:55 Intrinsic Computation in NEMSRussell Hawkins, University of California,

Davis, USA

2:00-2:25 Control of Complex Diffusion in Networks of NEMSJeff Emenheiser, University of California,

Davis, USA; Mehran Mesbahi, University of Washington, USA; Raissa D’Souza, University of California, Davis, USA

2:30-2:55 Phase Synchronization Between Nanoelectromechanical OscillatorsMatt Matheny, California Institute of

Technology, USA

Tuesday, May 19

MS61State and Parameter Estimation for Complex Dynamical Systems1:30 PM-3:30 PMRoom:Magpie A

Using mathematical models to analyze and predict real world dynamical processes meets with the difficulty that often not all state variables are easy to observe, and adequate values of model parameters may be (partly) unknown. To estimate unobserved variables and model parameters, various identification methods have been devised, aiming to match the model output to some observed time. This may be considered a form of data assimilation, a term which refers to incorporating observed data into computer models of the observed system. The presentations of this minisymposium will address theoretical issues, new concepts, and applications of state and parameter estimation techniques.

Organizer: Ulrich ParlitzMax Planck Institute for Dynamics and Self-Organization, Germany

Organizer: Henry D. AbarbanelUniversity of California, San Diego, USA

Organizer: Jochen BröckerUniversity of Reading, United Kingdom

1:30-1:55 What Is the Right Functional for Variational Data Assimilation?Jochen Bröcker, University of Reading,

United Kingdom

2:00-2:25 Filtering Unstable Quadratic Dissipative SystemsKody Law, King Abdullah University of

Science & Technology (KAUST), Saudi Arabia; Abhishek Shukla, Daniel Sanz-Alonso, and Andrew Stuart, University of Warwick, United Kingdom

2:30-2:55 Time Delay Methods for Variational Data AssimilationUriel I. Morone, University of California,

San Diego, USA

3:00-3:25 Observability of Chaotic Lorenz-96 SystemsJan Schumann-Bischoff, Stefan Luther,

and Ulrich Parlitz, Max Planck Institute for Dynamics and Self-Organization, Germany


Tuesday, May 19

MS66Stochastic and Nonlinear Dynamics of Neuronal Networks - Part I of II1:30 PM-3:30 PMRoom:Superior A

For Part 2 see MS74 Coherent neural activity patterns have been implicated as a substrate of short term memory, spatial navigation, sensation, and motor skills. Understanding the mechanisms that underlie this activity requires using sophisticated mathematical methods to analyze nonlinear models of neuronal networks. Recent advances along these lines address the effects of stochasticity, spatial heterogeneity, delays, and modular structure on the dynamics of neuronal networks. This session will feature talks on cutting-edge methods for analyzing stochastic neural field equations, balanced networks, and mean field theories for spiking networks.

Organizer: Zachary KilpatrickUniversity of Houston, USA

Organizer: Jonathan D. TouboulCollège de France, France

Organizer: Bard ErmentroutUniversity of Pittsburgh, USA

1:30-1:55 Finite Size Effects in Networks of Theta NeuronsSiwei Qiu and Carson C. Chow, National

Institutes of Health, USA

2:00-2:25 Optimal Decision-Making in a Changing EnvironmentAlan Veliz-Cuba, University of Houston

and Rice University, USA; Zachary Kilpatrick and Krešimir Josic, University of Houston, USA

2:30-2:55 A Computational Model of the Influence of Depolarization Block on Initiation of Seizure-like ActivityDuane Nykamp, University of Minnesota,

USA

3:00-3:25 Traveling Waves in a Laminar Neural Field Model of Visual CortexSamuel R. Carroll, University of Utah,

USA; Paul C. Bressloff, University of Utah, USA and University of Oxford, United Kingdom

Tuesday, May 19

MS65Spiral and Scroll Waves Dynamics in Experiment and Simulations - Part I of II1:30 PM-3:30 PMRoom:Maybird

For Part 2 see MS73 Spiral and scroll waves are nonlinear dissipative patterns occurring in 2- and 3-dimensional excitable and oscillatory media, where they act as organizing centers. Important motivation to study spiral and scroll waves dynamics is better control of cardiac re-entry underlying dangerous arrhythmias and fatal fibrillation. Though, the vortices become of increasing interest of their own as regimes of self-organisation and transition to chaos. Recent advances in experimental, theoretical and computer simulation techniques brought the studies closer to practical applications than ever before. This minisymposium provides a sampling of the current state of experimental and computer simulation research in this field.

Organizer: Irina BiktashevaUniversity of Liverpool, United Kingdom

1:30-1:55 Anatomy Induced Drift of Reentrant Waves in Human AtriumIrina Biktasheva, University of Liverpool,

United Kingdom; Vadim N. Biktashev and Sanjay R. Kharche, University of Exeter, United Kingdom; Gunnar Seemann, Karlsruhe Institute of Technology, Germany; Henggui Zhang, The University of Manchester, UK

2:00-2:25 Stabilized Wave Segments in An Excitable Medium with a Phase Wave at the Wave BackEberhard Bodenschatz and Vladimir

Zykov, Max-Planck-Institute for Dynamics and Self-Organization, Germany

2:30-2:55 Use of Delay-Differential Equations in Cardiac ModelsElizabeth M. Cherry, Cornell University,

USA; Ryan Thompson, Rochester Institute of Technology, USA

3:00-3:25 Spiral Wave Activity in a Mixture of Resting and Oscillating Cardiomyocytes: Limitations on Biopacemaker DevelopmentPhilippe Comtois, Université de Montréal,

Canada

Tuesday, May 19

MS64Excitation Waves in Heterogeneous Cardiac Tissue: Theory and Experiments1:30 PM-3:30 PMRoom:Wasatch B

In this minisymposium we plan to bring together experimentalists and theorist interested on the initiation and control of spiral waves in the cardiac system. From the dynamical system perspective cardiac tissue can be considered as an excitable medium. Indeed, experiments have shown that dynamics of cardiac excitation waves during fibrillation is similar to dynamics of spiral waves in excitable media. This perspective is already bearing fruits in understanding cardiac arrhythmias and its management. For example new defibrillation methods have been proposed using low energy pulses to eliminate spiral waves from heterogeneities in the cardiac tissue. This minisymposium will discuss some of the underlying theoretical issues and experimental challenges.

Organizer: Shajahan Thamara KunnathuMax Planck Institute for Dynamics and Self-Organization, Germany

1:30-1:55 Controlling Spiral Wave Dynamics in Cardiac Monolayers Using Far Field PulsesShajahan Thamara Kunnathu, Sebastian

Berg, Valentin Krinsky, and Stefan Luther, Max Planck Institute for Dynamics and Self-Organization, Germany

2:00-2:25 A Mechanism of Spiral Wave Unpinning and Its Implications for the Treatment of Cardiac Arrhythmias with Periodic Far-Field PacingPhilip Bittihn, University of California, San

Diego, USA; Anna Behrend and Stefan Luther, Max Planck Institute for Dynamics and Self-Organization, Germany

2:30-2:55 The Effects of Cardiac Fibroblasts on Wave Propagation in Ventricular Tissue: Insights from Numerical Studies of Mathematical ModelsAlok R. Nayak and Rahul Pandit, Indian

Institute of Science, Bangalore, India

3:00-3:25 How to Control Spiral Waves Using Weak Signals: A Few SuggestionsS Sridhar, Ghent University, Belgium


3:00-3:25 Synchronization and the problem of Targeting in Multilayer NetworksRicardo Gutierrez, Weizmann Institute

of Science, Israel; Irene Sendina Nadal, Universidad Rey Juan Carlos, Spain; Massimiliano Zanin, Technical University of Madrid, Spain; David Papo, Universidad Politécnica de Madrid, Spain; Stefano Boccaletti, CNR, Italy

Tuesday, May 19

MS68The Structure and Dynamics of Multilayer Networks1:30 PM-3:30 PMRoom:White Pine

Up until recently, network theory was almost exclusively limited to networks in which all components were treated on equivalent footing. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer a series of talks on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

Organizer: Stefano BoccalettiCNR, Italy

Organizer: Regino CriadoUniversidad Rey Juan Carlos, Spain

Organizer: Charo I. del GenioUniversity of Warwick, United Kingdom

Organizer: Irene Sendina NadalUniversidad Rey Juan Carlos, Spain

Organizer: Miguel RomanceUniversidad Rey Juan Carlos, Spain

Organizer: Zhen WangKyushu University, Japan

1:30-1:55 Characterizing the Structure of Multilayer NetworksRegino Criado and Miguel Romance,

Universidad Rey Juan Carlos, Spain

2:00-2:25 Game and Diffusion Dynamics in Multilayer NetworksZhen Wang, Kyushu University, Japan

2:30-2:55 Synchronization in Time Varying Networks: the Non Commutative CaseCharo I. del Genio, University of

Warwick, United Kingdom

Tuesday, May 19

MS67Evolutionary Dynamics and Constraints of Quickly Mutating Pathogens1:30 PM-3:30 PMRoom:Superior B

Understanding the evolution of pathogens is an important topic in science. High reproduction rates, large populations, high mutation and recombination rates, etc. are but some of the strategies pathogens adopt to escape selection pressure (immune response, drugs/therapies, etc.). Fast paced technological advances are allowing more and more high throughput experimental investigations, thus uncovering novel biological phenomena and providing large high-quality datasets. The aim of this minisymposium is to gather experts in the field of application of dynamical systems to theoretical evolutionary biology to assess determinants and constraints of rapidly evolving organisms in complex environments.

Organizer: Simone BiancoIBM Research, USA

1:30-1:55 Costs and Benefits of Mutational Robustness in Rna VirusesSimone Bianco, IBM Research, USA

2:00-2:25 Thermodynamics and Statistical Mechanics of Viral EvolutionBarbara Jones and James Kaufman, IBM

Research, USA; Justin Lessler, Johns Hopkins Bloomberg School of Public Health, USA

2:30-2:55 The Acceleration of Evolutionary Spread by Long-Range DispersalOskar Hallatschek, University of

California, Berkeley, USA

3:00-3:25 Evolutionary Dynamics of Mutator Phenotypes in Changing EnvironmentsOana Carja, University of Pennsylvania,

USA



Tuesday, May 19

MS71Emerging Collective Patterns in Dynamic Swarms4:00 PM-6:00 PMRoom:Ballroom I

Swarming dynamics are characterized by the emergence of complex motion patterns from simple interactions between individual agents. Understanding the mechanisms which drive the formation of these highly coherent motion pattern can lead to key insights into many processes in biology, such as the growth and development in multi-cellular organisms, and the collective motion of animal groups. Such an understanding should prove valuable for the development of algorithms to generate collective motions in engineered systems. This minisymposium will focus on recent advancements in biological swarming dynamics, as well as the application of these methods to swarming systems in engineering.

Organizer: Klementyna SzwaykowskaNaval Research Laboratory, USA

Organizer: Luis Mier-y-TeranJohns Hopkins Bloomberg School of Public Health, USA

4:00-4:25 Nonlocal Aggregation Models: A Primer of Swarm EquilibriaAndrew J. Bernoff, Harvey Mudd College,

USA; Chad M. Topaz, Macalester College, USA

4:30-4:55 Fire Ants Build, Morph, and Repair to Survive FloodsDavid Hu, Georgia Institute of Technology,

USA

5:00-5:25 Quantifying Collective Cell Migration During Cancer ProgressionRachel Lee, University of Maryland, College

Park, USA; Haicen Yue and Wouter-Jan Rappel, University of California, San Diego, USA; Wolfgang Losert, University of Maryland, College Park, USA

5:30-5:55 Aggregate Behaviors of Heterogeneous, Delay-Coupled AgentsKlementyna Szwaykowska, Naval Research

Laboratory, USA; Christoffer R. Heckman, University of Colorado Boulder, USA; Luis Mier-y-Teran, Johns Hopkins Bloomberg School of Public Health, USA; Ira B. Schwartz, Naval Research Laboratory, USA

Tuesday, May 19

MS70Recent Applications of Singular Perturbation Theory - Part I of II1:30 PM-3:30 PMRoom:Primrose B

For Part 2 see MS77 Singularly perturbed dynamical systems arise in many applications; for example, whenever there is a natural separation of time scales or a bifurcation that changes the underlying structure of a system. Many techniques have been developed to study such systems. Geometric singular perturbation methods use properties of “geometric” dynamical objects such as invariant manifolds and foliations. On the other hand, spectral techniques have been used to study transitions between linear operators that are posed on different spaces but are nevertheless “close’’. This minisymposium presents recent theoretical results for which singular perturbation theory plays a key role in the analysis.

Organizer: Kelly McquighanBoston University, USA

Organizer: Hermen Jan HupkesUniversity of Leiden, The Netherlands

Organizer: Peter van HeijsterQueensland University of Technology, Australia

1:30-1:55 Travelling Waves for Fully Discretized Bistable Reaction-Diffusion ProblemsHermen Jan Hupkes, University of Leiden,

The Netherlands

2:00-2:25 Oscillatory Pulses in FitzHugh-NagumoPaul A. Carter and Bjorn Sandstede, Brown

University, USA

2:30-2:55 Invariant Manifolds of Multi Interior Spike States for the Cahn-Hilliard EquationPeter W. Bates, Michigan State University,

USA

3:00-3:25 Slow-Fast Factorization of the Evans Function Via the Riccati Transformation in the Semi-Strong RegimeBjörn De Rijk and Arjen Doelman, Leiden

University, Netherlands; Jens Rademacher, University of Bremen, Germany


Tuesday, May 19

MS69Applications of Chaotic, Stochastic and Multiscale Dynamics1:30 PM-3:30 PMRoom:Primrose A

Chaotic, stochastic and multiscale processes are common in many areas of contemporary scientific applications, such as modeling in neuroscience, nonlinear optics, and geosciences, among others. Key topics of modeling for complex systems will be brought together in this interdisciplinary session. Two speakers will communicate their recent work in multiscale modeling for neuroscience and nonlinear optics. Two other participants will report their new findings in coarse-graining and response to stochastic perturbations of more general nonlinear systems.

Organizer: Rafail AbramovUniversity of Illinois, Chicago, USA

Organizer: Ibrahim FatkullinUniversity of Arizona, USA

1:30-1:55 The Response of Statistical Averages to Small Stochastic ForcingRafail Abramov, University of Illinois,

Chicago, USA

2:00-2:25 Is Our Sensing Compressed?Gregor Kovacic, Rensselaer Polytechnic

Institute, USA

2:30-2:55 A Multiscale Method for Optical Responses of Nano StructuresDi Liu, Michigan State University, USA

3:00-3:25 Parareal Methods for Highly Oscillatory Dynamical SystemsRichard Tsai, University of Texas,

Houston, USA


Tuesday, May 19

MS74Stochastic and Nonlinear Dynamics of Neuronal Networks - Part II of II4:00 PM-6:00 PMRoom:Superior A

For Part 1 see MS66 Coherent neural activity patterns have been implicated as a substrate of short term memory, spatial navigation, sensation, and motor skills. Understanding the mechanisms that underlie this activity requires using sophisticated mathematical methods to analyze nonlinear models of neuronal networks. Recent advances along these lines address the effects of stochasticity, spatial heterogeneity, delays, and modular structure on the dynamics of neuronal networks. This session will feature talks on cutting-edge methods for analyzing stochastic neural field equations, balanced networks, and mean field theories for spiking networks.

Organizer: Zachary KilpatrickUniversity of Houston, USA

Organizer: Jonathan D. TouboulCollège de France, France

Organizer: Bard ErmentroutUniversity of Pittsburgh, USA

4:00-4:25 Oscillations in Neuronal NetworksStefanos Folias, University of Alaska,

Anchorage, USA

4:30-4:55 Dynamics of Networks with Partially Symmetric Connectivity MatricesNicolas Brunel, University of Chicago,

USA

5:00-5:25 Assembling Collective Activity in Neural CircuitsEric Shea-Brown, University of

Washington, USA

5:30-5:55 On a Kinetic Fitzhugh-Nagumo EquationCristobal Quininao, Laboratoire Jacques-

Louis Lions, France

Tuesday, May 19

MS73Spiral and Scroll Waves Dynamics in Experiment and Simulations - Part II of II4:00 PM-6:00 PMRoom:Maybird

For Part 1 see MS65 Spiral and scroll waves are nonlinear dissipative patterns occurring in 2- and 3-dimensional excitable and oscillatory media, where they act as organizing centers. Important motivation to study spiral and scroll waves dynamics is better control of cardiac re-entry underlying dangerous arrhythmias and fatal fibrillation. Though, the vortices become of increasing interest of their own as regimes of self-organisation and transition to chaos. Recent advances in experimental, theoretical and computer simulation techniques brought the studies closer to practical applications than ever before. This minisymposium provides a sampling of the current state of experimental and computer simulation research in this field.

Organizer: Irina BiktashevaUniversity of Liverpool, United Kingdom

4:00-4:25 Crossover Collisions of Scroll WavesDennis Kupitz and Marcus Hauser, Otto-

von-Guericke University, Magdenburg, Germany

4:30-4:55 Role of Small Sized Heterogeneities in the Onset and Perpetuation of ArrhythmiasAlexander Panfilov, Arne Defauw, Nele

Vandersickel, and Peter Dawyndt, Ghent University, Belgium

5:00-5:25 Effects of Substrate Geometry on Spiral Wave ChiralityThomas D. Quail, Alvin Shrier, and Leon

Glass, McGill University, Canada

5:30-5:55 Scroll Waves in Viscous Systems with Stokes Flow: Writing Filaments and Other New TricksOliver Steinbock, Florida State University,

USA

Tuesday, May 19

MS72Synchronization of Chaos, Chimera and Neurosciences - Part II of II4:00 PM-6:00 PMRoom:Ballroom II

For Part 1 see MS59 Many fundamental processes in nature are based on synchronization of chaos. This phenomenon is universal, robust and it may also involve large population of active elements distributed over extensive spatial regions. In this minisymposium theoretical and application issues related to this phenomenon will be considered. In particular, we address the fundamental role that this phenomenon has in the organization of the collective movement, in neuroscience and in the development of scenarios that lead to coexistence of ordered and disordered states.

Organizer: Elbert E. MacauLaboratory for Computing and Applied Mathematics and Brazilian Institute for Space Research, Brazil

Organizer: Epaminondas RosaIllinois State University, USA

4:00-4:25 Nontrivial Collective Dynamics in Networks of Pulse Coupled OscillatorsAntonio Politi and Ekkehard Ullner,

University of Aberdeen, United Kingdom

4:30-4:55 Effects of Reciprocal Inhibitory Coupling in Synchronous NeuronsEpaminondas Rosa, Illinois State

University, USA

5:00-5:25 Clustering, Malleability and Synchronization of Hodgkin-Huxley-Type NeuronsSergio R. Lopes, Thiago de L. Prado,

Ricardo L. Viana, and José C. P. Coninck, Federal University of Paraná, Brazil; Juergen Kurths, Potsdam Institute for Climate Impact Research and Humboldt University Berlin, Germany

5:30-5:55 Synchronization in a Cortical Multilayered Computational Model: A Simulation StudyAntonio C. Roque, Renan O. Shimoura,

and Rodrigo F. O. Pena, University of Sao Paulo, Brazil


Tuesday, May 19

MS76Networks of Chemical Oscillators4:00 PM-6:00 PMRoom:Primrose A

Chemical oscillations, which are a remarkable nonequilibrium phenomenon, can be observed in chemical engineering applications and are ubiquitous in biological systems. The realization of networks of coupled chemical oscillators with control over the coupling function and topology is a challenging experimental task, even for small and intermediate network sizes. In this workshop we report on recent experiments in which the coupling between the oscillatory chemical reactions is realized via microfluid arrays, optical feedback or wired connections in electrochemical arrays. The experiments demonstrate the connection between the rich dynamical behavior and the network topology.

Organizer: Ralf ToenjesPotsdam University, Germany

4:00-4:25 Synchronization and Network Topology of Electrochemical Micro-Oscillators in On-Chip Integrated Flow CellsIstvan Z. Kiss, Yanxin Jia, Yifan Liu, and

Jasmine Coleman, Saint Louis University, USA

4:30-4:55 Microfluidic Networks of Belousov-Zhabotinsky DropsSeth Fraden, Brandeis University, USA

5:00-5:25 Synchronization in Networks of Coupled Chemical OscillatorsKenneth Showalter, West Virginia

University, USA

5:30-5:55 Long Transients to Synchronization in Random Networks of Electrochemical OscillatorsRalf Toenjes, Potsdam University,

Germany; Michael Sebek and Istvan Z. Kiss, Saint Louis University, USA

Tuesday, May 19

MS75Between Order and Chaos: Entropy and Information Processing in Complex Dynamics4:00 PM-6:00 PMRoom:Superior B

Complex systems often exhibit a fine balance between order and chaos. On one hand, high-dimensional deterministic dynamical systems can show sensitive dependence on initial conditions wile on the other, identifying sensible macroscopic physical observables relies on emergent coherent coarse-grained structures. The recent years have seen the application of information-theoretic aspects to a variety of complex dynamics, ranging from stochastic thermodynamics to neuroscience. In this symposium, we review some of these aspects and discuss relations between notions of entropy and information arising in various dynamical descriptions used in complexity science.

Organizer: Bernhard AltanerMax Planck Institute for Dynamics and Self-Organization, Germany

Organizer: Guillaume LajoieUniversity of Washington, USA

4:00-4:25 Entropy, Dissipation and Information Processing in Models of Complex SystemsBernhard Altaner, Max Planck Institute


4:30-4:55 Deconstructing Maxwell’s DemonDibyendu Mandal, University of

California, Berkeley, USA

5:00-5:25 Degrees of Information Processing in Chaotic Dynamical SystemsRyan G. James, University of California,

Davis, USA

5:30-5:55 Time-Dependent Chaotic Attractors Shape Information Content in Neural NetworksGuillaume Lajoie, University of

Washington, USA

Tuesday, May 19

MS77Recent Applications of Singular Perturbation Theory - Part II of II4:00 PM-6:00 PMRoom:Primrose B

For Part 1 see MS70 Singularly perturbed dynamical systems arise in many applications; for example, whenever there is a natural separation of time scales or a bifurcation that changes the underlying structure of a system. Many techniques have been developed to study such systems. Geometric singular perturbation methods use properties of “geometric” dynamical objects such as invariant manifolds and foliations. On the other hand, spectral techniques have been used to study transitions between linear operators that are posed on different spaces but are nevertheless “close’’. This minisymposium presents recent theoretical results for which singular perturbation theory plays a key role in the analysis.

Organizer: Kelly McquighanBoston University, USA

Organizer: Hermen Jan HupkesUniversity of Leiden, The Netherlands

Organizer: Peter van HeijsterQueensland University of Technology, Australia

4:00-4:25 Pinning and Unpinning in Nonlocal EquationsTaylor Anderson, Mount Holyoke College,

USA; Gregory Faye, École des Hautes Etudes en Sciences Sociales, France; Arnd Scheel, University of Minnesota, Minneapolis, USA; David Stauffer, Cornell University, USA

4:30-4:55 Singularities in Front Bifurcations with Scale SeparationJens Rademacher, University of Bremen,

Germany

5:00-5:25 Travelling Waves and Canards in a Model of Wound Healing AngiogenesisKristen Harley and Peter van Heijster,

Queensland University of Technology, Australia; Robert Marangell, University of Sydney, Australia; Graeme Pettet, Queensland University of Technology, Australia; Martin Wechselberger, University of Sydney, Australia

5:30-5:55 Canard SupersoniqueMartin Wechselberger, University of

Sydney, Australia


Tuesday, May 19

CP27Topics in Biological Dynamics IV4:00 PM-6:00 PMRoom:Magpie B

Chair: Linda Sommerlade, University of Aberdeen, United Kingdom

4:00-4:15 Analysis of Cholera Epidemics with Bacterial Growth and Spatial MovementXueying Wang, Washington State

University, USA

4:20-4:35 Optogenetic Stimulation of a Meso-Scale Human Cortical ModelPrashanth Selvaraj and Andrew J. Szeri,

University of California, Berkeley, USA; James W. Sleigh, University of Auckland, New Zealand; Heidi E. Kirsch, University of California, San Francisco, USA

4:40-4:55 Growth Dynamics for Pomacea MaculataLihong Zhao and Karyn L. Sutton,

University of Louisiana, Lafayette, USA; Jacoby Carter, USGS National Wetlands Research Center, USA

5:00-5:15 Assessing the Strength of Directed Influences Among Neural SignalsLinda Sommerlade and Marco Thiel,

University of Aberdeen, United Kingdom; Claude Wischik, TauRx Therapeutics Ltd., Singapore; Bjoern Schelter, University of Aberdeen, United Kingdom

5:20-5:35 Benefits of Noise in Synaptic Vesicle ReleaseCalvin Zhang and Charles S. Peskin,

Courant Institute of Mathematical Sciences, New York University, USA

5:40-5:55 Towards Understanding Mechanisms of Pain Transmission: a Systems Theoretic ApproachPierre Sacré and Sridevi Sarma, Johns

Hopkins University, USA

Tuesday, May 19

CP26Topics in Financial Dynamical Systems and Related Themes4:00 PM-5:00 PMRoom:Magpie A

Chair: To Be Determined

4:00-4:15 Constant Rebalanced Portfolio Strategy Is Rational in a Multi-Group Asset Trading ModelMark DeSantis, Chapman University, USA;

David Swigon, University of Pittsburgh, USA

4:20-4:35 How Monetary Policy Can Cause Forecasting UncertaintyJames M. Haley, Point Park University,

USA

4:40-4:55 Non-Smooth Dynamics and Bifurcations in a Model of Electricity MarketGerard Olivar Tost and Johnny Valencia

Calvo, Universidad Nacional de Colombia, Colombia

Tuesday, May 19

MS97Dynamical Models in Drug Delivery4:00 PM-6:00 PMRoom:Ballroom III

Mathematical modeling of drug delivery has been attracting great attention of scientists for years. It provides an adequate quantitative description of physical, chemical and biological processes that determine the performance of drug delivery systems. The goal of this minisymposium is to present recent advances in modeling basic types of drug delivery, including systems based on fluid flows, swelling and deswelling gels, liquid films, nanoparticles and lipid membranes, as well as transdermal drug delivery systems.

Organizer: Alexander NepomnyashchyTechnion - Israel Institute of Technology, Israel

Organizer: Vladimir VolperNorthwestern University, USA

4:00-4:25 Cyclic Drug Delivery Devices and Monotone Dynamical SystemsMaria-Carme Calderer, University of

Minnesota, USA

4:30-4:55 Evaluation of the Diffusion Coefficient of Nanoparticles Using Mathematical SimulationGiora Enden and Amnon Sintov, Ben-

Gurion University of the Negev, Israel

5:00-5:25 Fluid Flow and Drug Delivery in a Brain TumorRanadhir Roy and Daniel Riahi, University

of Texas - Pan American, USA

5:30-5:55 Viscoelastic Effects in Drug DeliveryAlexander Nepomnyashchy, Technion

- Israel Institute of Technology, Israel; Vladimir A. Volpert, Northwestern University, USA; Yulia Kanevsky, Technion - Israel Institute of Technology, Israel


Tuesday, May 19

PP1Poster Session and Dessert Reception8:30 PM-10:30 PMRoom:Ballroom

The Breakup of Invariant Tori in 4-D Maps Using the Slater’s CriterionCelso Abud and Ibere L. Caldas, University

of Sao Paulo, Brazil

Theta Model for Quartic Integrate-and-Fire Neuron ModelAkihiko Akao and Yutaro Ogawa, University

of Tokyo, Japan; Bard Ermentrout, University of Pittsburgh, USA; Yasuhiko Jimbo and Kiyoshi Kotani, University of Tokyo, Japan

A Solution of Linear Programming Problems with Interval CoefficientsIbraheem Alolyan, King Saud University,

Saudia Arabia

Developing a Model Approximation Method and Parameter Estimates for a Solar Thermochemistry ApplicationWilliam D. Arloff, Karl Schmitt, Luke

Venstrom, and Leandro Jaime, Valparaiso University, USA

Hamiltonian Hopf Bifurcations in Schrödinger TrimersCasayndra H. Basarab and Roy Goodman,

New Jersey Institute of Technology, USA

Computing the Optimal Path in Stochastic Dynamical SystemsMartha Bauver, Lora Billings, and Eric

Forgoston, Montclair State University, USA

Effects of Quasi-Steady-State Reduction on Biophysical Models with OscillationsSebastian D. Boie, Vivien Kirk, and James

Sneyd, University of Auckland, New Zealand

Analyzing Cycling Dynamics in Stochastic SystemsPralhad Burli, Lora Billings, and Eric


Limit Cycles in a Simplified Basal Ganglia ModelMichael Caiola and Mark Holmes,

Rensselaer Polytechnic Institute, USA

Tuesday, May 19

CP29Topics in Pattern Formation II4:00 PM-5:20 PMRoom:Wasatch B

Chair: Víctor Brena-Medina, University of Bristol, United Kingdom

4:00-4:15 Symmetry Groups and Dynamics of Time-Fractional Diffusion EquationMuhammad D. Khan, Institute of Business

Management, Pakistan

4:20-4:35 Polynomial Mixing Rates of Particle SystemsYao Li, Courant Institute of Mathematical

Sciences, New York University, USA

4:40-4:55 Stripe to Spot Transition in a Plant Root Hair Initiation ModelVictor F. Brena-Medina, University

of Bristol, United Kingdom; Daniele Avitabile, University of Nottingham, United Kingdom; Alan R. Champneys, University of Bristol, United Kingdom; Michael Ward, University of British Columbia, Canada

5:00-5:15 Onset of Singularities in the Pattern of Fluctuational Paths of a Nonequilibrium SystemOleg B. Kogan, Cornell University,

USA; Mark I. Dykman, Michigan State University, USA


SIADS Editorial Board Meeting6:30 PM-8:30 PMRoom: Summit Room

Tuesday, May 19

CP28Topics in Feedback/Control/Optimization II4:00 PM-5:00 PMRoom:Wasatch A

Chair: Raya Horesh, IBM T.J. Watson Research Center, USA

4:00-4:15 Towards a Structural Theory of Controllability of Binary NetworksAfroza Shirin, University of New Mexico,

USA

4:20-4:35 Optimal Treatment Strategies for HIV-TB Co-Infected IndividualsAbhishek Mallela, University of Missouri,

Kansas City, USA; Suzanne M. Lenhart, University of Tennessee, USA; Naveen K. Vaidya, University of Missouri, Kansas City, USA

4:40-4:55 Optimal Control of Building’s Hvac System with on-Site Energy Storage and Generation SystemRaya Horesh, Young M. Lee, and Leo

Liberti, IBM T.J. Watson Research Center, USA; Young Tae Chae, Hyundai Engineering & Construction Co., Ltd, Korea; Rui Zhang, IBM T.J. Watson Research Center, USA



Discriminating Chaotic and Stochastic Dynamics Through the Permutation Spectrum TestChristopher W. Kulp, Lycoming College,

USA; Luciano Zunino, Centro de Investigaciones en Optica, Mexico

Coupling Methods As a Tool for Sensitivity Analysis of Stochastic Differential EquationsAndrew Leach, University of Arizona, USA

Transient Dynamics in Ensemble of Inhibitory Coupled Rulkov MapsTatiana A. Levanova and Grigory Osipov,

Lobachevsky State University of Nizhny Novgorod, Russia

Complex Collective Behavior in a Network of Theta Neurons is Suppressed by Synaptic DiversityLucas Lin, Thomas Jefferson High School

of Science and Techonology, USA; Paul So and Ernest Barreto, George Mason University, USA

Shape Coherence and Finite-Time Curvature Evolution in Time-Dependent Dynamical SystemsTian Ma and Erik Bollt, Clarkson University,

USA

Snaking on Networks: From Local Solutions to Turing PatternsNick McCullen, University of Bath,

United Kingdom; Matthias Wolfrum, Weierstrass Institute for Applied Analysis and Stochastics, Germany; Thomas Wagenknecht, University of Leeds, United Kingdom

Fractal Boundaries in the Parameters Space of Deterministic Dynamical SystemsEverton S. Medeiros, University of

Sao Paulo, Brazil; Iberê L. Caldas, Universidade de Sao Paulo, Brazil; Murilo Baptista, University of Aberdeen, United Kingdom

A Biophysical Model for the Role of Network Topology in Regulating a Two-Phase Breathing RhythmJoshua Mendoza, Kameron Decker

Harris, and Eric Shea-Brown, University of Washington, USA; Jan Ramirez and Tatiana Dashevskiy, Seattle Children’s Research Institute, USA

Modeling Effects of Drugs of Abuse on Hiv-Specific Antibody ResponsesJones M. Mutua, Anil Kumar, and Naveen

K. Vaidya, University of Missouri, Kansas City, USA

Spike Adding in Transient DynamicsSaeed Farjami, Hinke M. Osinga, and

Vivien Kirk, University of Auckland, New Zealand

Front-Dynamics and Pattern Selection in the Wake of Triggered InstabilitiesRyan Goh and Arnd Scheel, University of

Minnesota, USA

Pattern Sequences as Early-warning Signs of Critical Transition in Models of Dryland VegetationKarna V. Gowda, Yuxin Chen, Sarah Iams,

and Mary Silber, Northwestern University, USA

Rigorous Computation of Radially Symmetric Stationary Solutions of PdesChris M. Groothedde, VU University,


Dynamics of Register Transitions in Human Vocal Fold ModelingJesse Haas, Grenoble University, France

A Mathematical Model of Saliva Secretion and Calcium DynamicsJung Min Han, James Sneyd, and Vivien

Kirk, University of Auckland, New Zealand

Mixed-Mode Oscillations and Twin CanardsRagheb Hasan, Hinke M. Osinga, and

Bernd Krauskopf, University of Auckland, New Zealand

A Dynamical Analysis of Steam Supply Network Based on Invariant ManifoldHikaru Hoshino and Yoshihiko Susuki,

Kyoto University, Japan

Defects in Spatially Extended SystemsGabriela Jaramillo, University of

Minnesota, USA; Arnd Scheel, University of Minnesota, Minneapolis, USA

Delayed Feedback Model of Axonal Length SensingBhargav R. Karamched, University of

Utah, USA; Paul C. Bressloff, University of Utah, USA and University of Oxford, United Kingdom

Nonlinear Dynamical Systems in FinanceDeniz K. Kiliç, Middle East Technical

University, Turkey

Tuesday, May 19


cont.

Mathematical Modelling of Spatial Sorting and Evolution in a Host-Parasite SystemMatthew H. Chan, Gregory Brown,

Richard Shine, and Peter S. Kim, University of Sydney, Australia

New Computational Tools for Non-Smooth Dynamical SystemsAntonio S. Chong and Marian Wiercigroch,

University of Aberdeen, United Kingdom

Polyrhythmic Synchronization in Modular NetworksJarod Collens, Justus T. Schwabedal, Andrey

Shilnikov, and Drake Knapper, Georgia State University, USA

Modeling the Lymphocytic Choriomeningitis Virus: Insights into Understanding Its Epidemiology in the WildChristy Contreras, Arizona State

University, USA

Causal Relationships Between Time Series: Generalizing Takens’ Theorem to a Dynamical NetworkBree Cummins and Tomas Gedeon,

Montana State University, USA; Kelly Spendlove, Rutgers University, USA

Regular Acceleration from Low Initial Energies in a Magnetized Relativistic SystemMeirielen C. De Sousa and Iberê L.

Caldas, Universidade de Sao Paulo, Brazil; Fernanda Steffens, Deutsches Elektronen-Synchrotron, Germany; Renato Pakter and Felipe Rizzato, Universidade Federal do Rio Grande do Sul, Brazil

Estimating the L∞-Norm of Linear Solutions of Cahn-HilliardPhilipp Düren, Universität Augsburg,

Germany

continued in next column continued on next page


Wednesday, May 20


MS78Dynamics of Moreau Sweeping Processes - Part I of II8:30 AM-10:30 AMRoom:Ballroom I

For Part 2 see MS91 A sweeping process describes the motion of a particle which is governed by a differential equation on the one hand and which is constrained by a moving convex set on the other hand. Such a configuration leads to a differential inclusion with unbounded right-hand-terms (Clarke normal cones). Building upon the discrete approximation scheme proposed my Moreau in 70th the theory of sweeping processes is now able to analyse the existence, continuous dependence, periodicity and (Lyapunov) stability of solutions. This minisymposium accumulates current achievements aiming to approach the structural stability and to understand how the dynamics changes under varying parameters (control).

Organizer: Oleg MakarenkovUniversity of Texas at Dallas, USA

8:30-8:55 On the Response of Sweeping Processes to PerturbationMikhail Kamenski, Voronezh State University,

Russia; Oleg Makarenkov, University of Texas at Dallas, USA

9:00-9:25 Dynamics of Sweeping Processes with Jumps in the Driving TermVincenzo Recupero, Politecnico di Torino,

Italy

9:30-9:55 Control of Moreau’s Sweeping Process: Some Results and Open ProblemsGiovanni Colombo, University of Padova,

Italy

10:00-10:25 Estimation and Control Problems in Systems with Moreau’s Sweeping ProcessAneel Tanwani, University of Kaiserslautern,

Germany

Robust Pulse Generators in An Excitable MediumTakashi Teramoto, Asahikawa Medical

University, Japan

Dynamical Building Blocks in Turbulent Two-Dimensional Channel FlowToshiki Teramura and Sadayoshi Toh,

Kyoto University, Japan

Phase Models and Oscillators with Time Delayed All-to-All CouplingZhen Wang, University of Waterloo,

Canada

Efficient Design of Navigable NetworksB.M. Shandeepa D. Wickramasinghe and

Jie Sun, Clarkson University, USA

Instability of Certain Equilibrium Solutions of the Euler Fluid EquationsJoachim Worthington, Holger R. Dullin,

and Robby Marangell, University of Sydney, Australia

A Symbolic Method in Chua’s CircuitTingli Xing and Andrey Shilnikov, Georgia


Interactions of Solitary Modes in Models of Bacterial ChemotaxisGlenn S. Young, Hanna Salman, Bard

Ermentrout, and Jonathan Rubin, University of Pittsburgh, USA

The Spread of Activity with Refractory Periods over Directed NetworksDaniel R. Zavitz and Alla Borisyuk,

University of Utah, USA

Using Tangles to Quantify Topological Mixing of FluidsQianting Chen, Sulimon Sattari, and Kevin

A. Mitchell, University of California, Merced, USA

Computing Chaotic Transport Properties in a Mixed Phase Space with Periodic OrbitsSulimon Sattari and Kevin A. Mitchell,

University of California, Merced, USA

Time-Delayed Model of Immune Response in PlantsGiannis Neofytou and Konstantin Blyuss,

University of Sussex, United Kingdom

Analysis and Control of Pre-Extinction Dynamics in Stochastic PopulationsGarrett Nieddu, Lora Billings, and Eric


An Explicit Formula for R0 of Tick-Borne Relapsing FeverCody Palmer, University of Montana, USA

Title Not AvailableYoungmin Park, University of Pittsburgh,

USA

Stochastic Motion of Bumps in Planar Neural FieldsDaniel Poll and Zachary Kilpatrick,

University of Houston, USA

Automatically Proving Periodic Solutions to Polynomial ODEsElena Queirolo, Vrije Universiteit

Amsterdam, The Netherlands

Repulsive Inhibition Promotes Synchrony in Excitatory Networks of Bursting NeuronsReimbay Reimbayev and Igor Belykh,

Georgia State University, USA

Quasipatterns in Two and Three DimensionsAlastair M. Rucklidge, University of

Leeds, United Kingdom

Rigorous Computations for BVPs with Chebyshev-seriesRay Sheombarsing, VU University,


Central Configurations of Symmetrically Restricted Five-Body ProblemAnoop Sivasankaran, Khalifa University

of Science, Technology and Research, United Arab Emirates; Muhammad Shoaib and Abdulrehman Kashif, University of Hail, Saudi Arabia

Finite Time Diagnostics and Transport Barriers in Non Twist SystemsJose D. Szezech Jr, Ponta Grossa State

University, Brazil; Ibere L. Caldas, University of Sao Paulo, Brazil; Sergio R. Lopes and Ricardo L. Viana, Federal University of Paraná, Brazil; Philip Morrison, University of Texas at Austin, USA



Wednesday, May 20

MS81First Passage Times in Discrete and Continuous Systems - Part I of II8:30 AM-10:30 AMRoom:Magpie A

For Part 2 see MS94 Numerous problems in nature are formulated in terms of Mean First Passage Time (MFPT) of Brownian particles in the presence of traps. For example, cells are regulated by chemical reactions involving signaling molecules that have to find their targets in a complex and crowded environment. The study of MFPT touches upon many topics and utilizes diverse tools including PDEs, stochastic differential equations, complex variables, generating functions and many others. This mini-session will bring together experts in this active field of research. Directions that will be considered include: search-and-rescue, mobile traps, narrow escape problems on bounded domains, connections to spike solutions of PDEs, and applications in biology and physics.

Organizer: Alan E. LindsayUniversity of Notre Dame, USA

Organizer: Justin C. TzouDalhousie University, Canada

8:30-8:55 First Passage Times in Biological Self-AssemblyMaria D’Orsogna, California State

University, Northridge, USA; Tom Chou, University of California, Los Angeles, USA

9:00-9:25 Asymptotic Analysis of Narrow Escape Problems in Non-Spherical 3D DomainsAlexei F. Cheviakov, University of

Saskatchewan, Canada; Daniel Gomez, University of British Columbia, Canada

9:30-9:55 Signal Focusing Through Active TransportAljaz Godec and Ralf Metzler, Universität

Potsdam, Germany

10:00-10:25 First-Passage Times of Random Walks in Confined GeometriesOlivier Benichou, Université Pierre et Marie

Curie, France

Wednesday, May 20

MS80Theoretical Aspects of Spiral and Scroll Wave Dynamics - Part I of II8:30 AM-10:30 AMRoom:Ballroom III

For Part 2 see MS93 Spiral and scroll waves are the most common types of solutions characterizing the dynamics of 2- and 3-dimensional excitable media such as the cardiac tissue. This minisymposium presents a sampling of recent analytical and numerical studies focusing on the interaction of scroll and spiral waves with perturbations such as structural heterogeneities and external stimuli as well as self-interactions and interaction of different spiral/scroll waves with each other.

Organizer: Roman GrigorievGeorgia Institute of Technology, USA

Organizer: Vadim N. BiktashevUniversity of Exeter, United Kingdom

8:30-8:55 Drift of Scroll Waves in Thin Layers Caused by Thickness FeaturesIrina Biktasheva, University of Liverpool,

United Kingdom; Hans Dierckx, Ghent University, Belgium; Vadim N. Biktashev, University of Exeter, United Kingdom

9:00-9:25 Spiral PinballsJacob Langham and Dwight Barkley,

University of Warwick, United Kingdom

9:30-9:55 Tidal Forces Act on Cardiac FilamentsHans Dierckx, Ghent University, Belgium

10:00-10:25 Computation of Unstable Solutions of Cardiac Models on Static and Evolving DomainsChristopher Marcotte and Roman Grigoriev,


Wednesday, May 20

MS79Topological Fluid and Mass Dynamics - Part I of II8:30 AM-10:30 AMRoom:Ballroom II

For Part 2 see MS92 Topological and geometrical methods provide powerful tools for predicting and interpreting the dynamics of fluid flows and interacting masses. This minisymposium will explore recent developments in the use of these methods for considering relative equilibria, modeling interaction dynamics on surfaces, and characterizing structure and transport in complex flows. This minisymposium is dedicated to Konrad Bajer (1956-2014), who made many contributions in this area.

Organizer: Stefanella BoattoUniversidade Federal do Rio De Janeiro, Brazil

Organizer: Mark A. StremlerVirginia Tech, USA

8:30-8:55 Eulerian Geometric Integration of Fluids for Computer GraphicsMathieu Desbrun, California Institute

of Technology, USA; Dmitry Pavlov, Imperial College London, United Kingdom; Evan S. Gawlik, Stanford University, USA; Yiying Tong, Michigan State University, USA; Gemma Mason, California Institute of Technology, USA; Eva Kanso, University of Southern California, USA

9:00-9:25 Poincare-Birkhoff Normal Forms for Hamiltonian Relative EquilibriaCristina Stoica, Wilfrid Laurier University,

Canada

9:30-9:55 The Dynamics of Vortices and Masses over Surfaces of Revolution Stefanella Boatto and Gladston Duarte,

Universidade Federal de Rio de Janeiro, Brazil; David G. Dritschel, University of St. Andrews, United Kingdom; Teresa J. Stuchi, Universidade Federal de Rio de Janeiro, Brazil; Carles Simo, Universitat de Barcelona, Spain; Rodrigo Schaefer, Universitat Politecnica de Catalunya, Spain

10:00-10:25 Studies on Dynamics of Vortices on a Flat TorusHumberto H. de Barros Viglioni,

Universidade Federal de Sergipe, Brazil


Wednesday, May 20

MS84Dynamics of Neural Networks with General Connectivity and Nonlinearity8:30 AM-10:30 AMRoom:Wasatch B

The dynamics of a neural field model can be analyzed using a nonlinear integro-differential equation. Two basic components in this model are the integral kernel, which models the network connectivity, and the nonlinear gain function. Many previous results are obtained under rather restrictive assumptions on the connectivity and the gain. In this minisymposium, we will present some recent theoretical as well as experimental works for more general types of connectivity functions and gain functions. The talks will discuss analytical tools for and dynamical consequences of generalizations such as anisotropy/inhomogeneity in the connectivity functions and non-monotonicity in the gain functions.

Organizer: Dennis YangDrexel University, USA

8:30-8:55 Asymmetric Stationary Bumps in Neural Field ModelsDennis Yang, Drexel University, USA

9:00-9:25 Homogenization Theory for Neural Field ModelsJohn Wyller, Norwegian University of Life

Sciences, Norway

9:30-9:55 Traveling Patterns in Lateral Inhibition Neural NetworksYixin Guo and Aijun Zhang, Drexel

University, USA

10:00-10:25 Modulating Synaptic Plasticity Within In Vitro Hippocampal NetworksRhonda Dzakpasu, Georgetown University,

USA

Wednesday, May 20

MS83Wave Propagation in Highly Nonlinear Dispersive Media - Part I of II8:30 AM-10:30 AMRoom:Wasatch A

For Part 2 see MS96 Wave propagation in highly nonlinear dispersive media has recently attracted considerable attention of the interdisciplinary community that includes applied mathematicians, physicists and engineers. In particular, dynamics of granular crystals has been a subject of intensive theoretical and experimental research because of their unique, adaptive dynamical properties. Strongly nonlinear dispersive media may exhibit quite intriguing phenomena such as broadband absorption, high-rate wave attenuation and strong energy localization, rendering them highly attractive for multiple engineering applications. In this minisymposium, leading experts dealing with this class of dynamical systems will come together for a creative exchange of ideas involving fundamental and applied research.

Organizer: Anna VainchteinUniversity of Pittsburgh, USA

Organizer: Yuli StarosvetskyTechnion - Israel Institute of Technology, Israel

8:30-8:55 Granular Acoustic Switches and Logic ElementsJinkyu Yang and Feng Li, University of

Washington, USA; Paul Anzel, California Institute of Technology, USA; Panayotis Kevrekidis, University of Massachusetts, USA; Chiara Daraio, ETH Zürich, Switzerland and California Institute of Technology, USA

9:00-9:25 Nonlinear Waves in Microsphere-Based MetamaterialsNicholas Boechler, University of

Washington, USA

9:30-9:55 Multiscale Analysis of Strongly Localized WavesGuillaume James, Université de Grenoble

and CNRS, France

10:00-10:25 Standing Waves on Tadpole GraphsDmitry Pelinovsky, McMaster University,

Canada

Wednesday, May 20

MS82Control of Multiscale Dynamics - Part I of II8:30 AM-10:30 AMRoom:Magpie B

For Part 2 see MS95 The control of dynamical systems has been extensively studied in the past century, which led to significant applications such as space mission, aerocraft design, or nanoelectromechanical systems. Multiscale simulation and modeling, on the other hand, has become an active field in recent years, due to the multiscale nature of complex systems ubiquitous in practical applications. We consider it an emerging direction to go further and control multiscale systems, which was not possible without contemporary multiscale methods and computational architectures. The proposed minisymposium gathers researchers working on frontiers of related fields, with goals of shaping this new direction and contributing to important applications.

Organizer: Molei TaoGeorgia Institute of Technology, USA

8:30-8:55 Control of Multiscale Dynamical SystemsRichard D. Braatz, Massachusetts Institute

of Technology, USA

9:00-9:25 Some Results on the Backward Stability of Singular Perturbation Approximations of Linear and Nonlinear Stochastic Control SystemsCarsten Hartmann, Free University


9:30-9:55 Variational Integrators for Multiscale DynamicsSina Ober-Bloebaum, University of

Paderborn, Germany; Sigrid Leyendecker, University of Erlangen-Nuremberg, Germany

10:00-10:25 Control of Oscillators, Temporal Homogenization, and Energy Harvest by Super-Parametric ResonanceMolei Tao, Georgia Institute of Technology,

USA


Wednesday, May 20

MS87Nonsmooth Dynamical Systems: Theory and Applications - Part I of II8:30 AM-10:30 AMRoom:Superior B

For Part 2 see MS100 Many physical systems involve abrupt events, such as switches, impacts or thresholds, and are well-modelled by equations that are nonsmooth. This minisymposium will discuss novel applications of nonsmooth systems in ecology, optics and neuroscience, as well as describe new developments in the theory of nonsmooth systems. Overall the talks will highlight the various nuances of nonsmooth systems and show how these relate to the dynamical behaviour of the physical systems being modelled.

Organizer: David J. SimpsonMassey University, New Zealand

8:30-8:55 Infinitely Many Coexisting Attractors in the Border-Collision Normal FormDavid J. Simpson, Massey University, New

Zealand

9:00-9:25 Geometric Optics and Piecewise Linear SystemsPaul Glendinning, University of

Manchester, United Kingdom

9:30-9:55 Analysis of Traveling Pulses and Fronts in a Nonsmooth Neural Mass ModelJeremy D. Harris, University of Pittsburgh,

USA

10:00-10:25 Are Plankton Discontinuous, Smooth Or Slow-Fast (and Furious)?Sofia Piltz, University of Oxford, United

Kingdom

Wednesday, May 20

MS86Front Propagation in Advection-Reaction-Diffusion Systems - Part I of II8:30 AM-10:30 AMRoom:Superior A

For Part 2 see MS99 Autocatalytic reactions in a spatially-extended system are characterized by the propagation of reaction fronts separating the species. The front dynamics is generally well-understood for reaction-diffusion systems in the absence of substrate flow. The effects of fluid motion on fronts in the general advection-reaction-diffusion (ARD) case have only recently received significant attention, despite the wide applicability of ARD, including microfluidic chemical reactors, plasmas, ecosystem dynamics in the oceans (e.g., plankton blooms), cellular- and embryonic-scale biological processes. This minisymposium brings together groups studying ARD systems from a variety of perspectives, including experiments, dynamical systems theory, numerical PDEs, and analytics.

Organizer: Kevin A. MitchellUniversity of California, Merced, USA

Organizer: Thomas H. SolomonBucknell University, USA

Organizer: John R. MahoneyUniversity of California, Merced, USA

8:30-8:55 Front Pinning in Single Vortex FlowsJohn R. Mahoney and Kevin A. Mitchell,


9:00-9:25 Front Propagation in Cellular Flows for Fast Reaction and Small DiffusivityAlexandra Tzella, University of Birmingham,

United Kingdom; Jacques Vanneste, University of Edinburgh, United Kingdom

9:30-9:55 Experimental Studies of Burning Invariant Manifolds as Barriers to Reaction FrontsSavannah Gowen, Mount Holyoke College,

USA; Tom Solomon, Bucknell University, USA

10:00-10:25 Propagation of An Autocatalytic Reaction Front in Heterogeneous Porous MediaLaurent Talon, Université Paris-Sud, France;

Dominique Salin, University of Pittsburgh School of Medicine, USA

Wednesday, May 20

MS85Advances in Viral Infection Modeling - Part I of II8:30 AM-10:30 AMRoom:Maybird

For Part 2 see MS98 Viral infections, be they acute, like influenza or ebola, or chronic, like HIV, pose a continuing threat to daily life. In recent years mathematical modeling has become an important tool in investigating these infections, and novel methods are rapidly emerging. The primary goal of this minisymposium is to provide a platform for discussion of mathematical advances in viral infection modeling and resulting insights into viral infections, at both the within-host and between-hosts (epidemiological) scales.

Organizer: Jessica M. ConwayPennsylvania State University, USA

Organizer: Naveen K. VaidyaUniversity of Missouri, Kansas City, USA

8:30-8:55 A Multi-Scale Model of Multiple Exposures to a PathogenJane Heffernan and Redouane Qesmi, York

University, Canada; Jianhong Wu, York University, Canada

9:00-9:25 Contact Network Models for Immunizing InfectionsShweta Bansal, Georgetown University,

USA

9:30-9:55 Evaluation of Combined Strategies for Controlling Dengue FeverAlun Lloyd, North Carolina State University,

USA

10:00-10:25 Mathematical Models of the Spatial and Evolutionary Dynamics of Influenza AJulia R. Gog, University of Cambridge,

United Kingdom


Wednesday, May 20

MS90Sensitivity Methods with Applications8:30 AM-10:30 AMRoom:Primrose B

Sensitivity and uncertainty analysis are used to understand the role of variability inherent in the physical experimentation, mathematical interpretation and mathematical analysis. We are interested in biological applications where uncertainty arises in each aspect of the joint experimental and theoretical studies. For example, immune response to bacterial challenge has stochastic elements. Additionally all experiments have limited precision in measuring the data, making parameter estimation challenging. Finally, model analysis typically requires approximation such as perturbation or numerical methods. We focus on methods for quantifying uncertainty in biological processes, the sensitivity of the model with respect to parameters and data assimilation methods.

Organizer: Nick CoganFlorida State University, USA

8:30-8:55 Using Sensitivity Analysis to Understand S. aureus InfectionsAngela M. Jarrett, Nick Cogan, and M

Yousuff Hussaini, Florida State University, USA

9:00-9:25 Computational Aspects of Stochastic Collocation with Multi-Fidelity ModelsXueyu Zhu and Dongbin Xiu, University of

Utah, USA

9:30-9:55 The Dynamics of Alopecia AreataAtanaska Dobreva, Florida State

University, USA; Ralf Paus, University of Manchester, United Kingdom and University of Münster, Germany; Nicholas Cogan, Florida State University, USA

10:00-10:25 Epistemic Uncertainty Quantification Using Fuzzy Set TheoryYanYan He and Dongbin Xiu, University of

Utah, USA


Wednesday, May 20

MS89Complex Network Theory Based Approaches in the Analyses of Complex Systems and Data - Part I of II8:30 AM-10:30 AMRoom:Primrose A

For Part 2 see MS102 Analysis of network data obtained from a complex system is often a challenging task. In this minisymposium we will be discussing few novel approaches for obtaining insights into the structural and functional properties of empirical networks and networks inferred from data. One of our focus areas will be to employ simulation of variety of dynamical processes on networks to study properties of empirical networks. We will also discuss methodologies to overcome problems in the analysis of empirical networks due to spurious or missing links. Dynamical system based approaches for transforming data into a network representing will also be presented.

Organizer: Nishant MalikUniversity of North Carolina at Chapel Hill, USA

8:30-8:55 Role of Netwok Topology in Collective Opinion FormationNishant Malik, University of North

Carolina at Chapel Hill, USA

9:00-9:25 Network Reliability As a Tool for Using Dynamics to Probe Network StructureStephen Eubank, Yasamin Khorramzadeh,

Mina Youssef, Shahir Mowlaei, and Madhurima Nath, Virginia Tech, USA

9:30-9:55 Linear Dynamics on Brain Networks: A Tool for Understanding CognitionDanielle Bassett, University of Pennsylvania,

USA and Fabio Pasqualetti, University of California, Riverside, USA

10:00-10:25 Dynamical Macro-Prudential Stress Testing Using Network TheoryDror Y. Kenett, Boston University, USA

Wednesday, May 20

MS88Emergent Phenomena from Many-player Dynamics in Biological and Social Systems8:30 AM-10:30 AMRoom:White Pine

Systems wherein the behavior of individual organisms is controlled by simple interaction rules, such as from discrete games, can lead to organized large scale dynamics. The global behavior can depend heavily on small nuances in the underlying interaction rules, as well as the network and/or structure on which these organisms reside. In this minisymposium, we will explore the dynamics that arise from various biological and social interactions within systems comprised of large numbers of agents.

Organizer: Scott MccallaMontana State University, USA

Organizer: Martin ShortGeorgia Institute of Technology, USA

8:30-8:55 Hotspots in a Non-Local Crime ModelScott Mccalla, Montana State University,

USA; Jonah Breslau, Pomona College, USA; Sorathan Chaturapruek, Harvey Mudd College, USA; Theodore Kolokolnikov, Dalhousie University, Canada; Daniel Yazdi, University of California, Los Angeles, USA

9:00-9:25 Co-Dimension One Self AssemblyJames von Brecht, California State

University, Long Beach, USA; Scott Mccalla, Montana State University, USA; David T. Uminsky, University of San Francisco, USA

9:30-9:55 Swarming of Self-propelled Particles in FluidsYaoli Chuang and Maria D’Orsogna,

California State University, Northridge, USA

10:00-10:25 Origin and Structure of Dynamic Social Networks Based on Cooperative ActionsChristoph Hauert and Lucas Wardil,

University of British Columbia, Canada


Wednesday, May 20

MS92Topological Fluid and Mass Dynamics - Part II of II1:30 PM-3:30 PMRoom:Ballroom II

For Part 1 see MS79 Topological and geometrical methods provide powerful tools for predicting and interpreting the dynamics of fluid flows and interacting masses. This minisymposium will explore recent developments in the use of these methods for considering relative equilibria, modeling interaction dynamics on surfaces, and characterizing structure and transport in complex flows. This minisymposium is dedicated to Konrad Bajer (1956-2014), who made many contributions in this area.

Organizer: Stefanella BoattoUniversidade Federal do Rio De Janeiro, Brazil

Organizer: Mark A. StremlerVirginia Tech, USA

1:30-1:55 Braid Dynamics, Self-organized Criticality, and Solar Coronal HeatingMitchell Berger, University of Exeter,

United Kingdom

2:00-2:25 Topological Shocks in Burgers TurbulenceKostantin Khanin, University of Toronto,

Canada

2:30-2:55 Topology of Vortex Trajectories in Wake-Like FlowsMark A. Stremler, Virginia Tech, USA

3:00-3:25 Characterizing Complexity of Aperiodic Braids of TrajectoriesMarko Budisic and Jean-Luc Thiffeault,

University of Wisconsin, Madison, USA

Wednesday, May 20

MS91Dynamics of Moreau Sweeping Processes - Part II of II1:30 PM-3:30 PMRoom:Ballroom I

For Part 1 see MS78 A sweeping process describes the motion of a particle which is governed by a differential equation on the one hand and which is constrained by a moving convex set on the other hand. Such a configuration leads to a differential inclusion with unbounded right-hand-terms (Clarke normal cones). Building upon the discrete approximation scheme proposed my Moreau in 70th the theory of sweeping processes is now able to analyse the existence, continuous dependence, periodicity and (Lyapunov) stability of solutions. This minisymposium accumulates current achievements aiming to approach the structural stability and to understand how the dynamics changes under varying parameters (control).

Organizer: Oleg MakarenkovUniversity of Texas at Dallas, USA

1:30-1:55 Sweeping Process and Congestion Models for Crowd MotionJuliette Venel, Universite Lille-Nord de

France, France

2:00-2:25 Evolution Equations Governed by Sweeping Processes and Applications in Heat Equations with Controlled ObstaclesHoang Nguyen, University of Technical

Federical Santa Maria, Chile

2:30-2:55 Periodic Solutions of Moreau Sweeping Processes and ApplicationsIvan Gudoshnikov, University of Texas at

Dallas, USA

3:00-3:25 Moreau Sweeping Processes on Banach SpacesMessaoud Bounkhel, King Saud

University, Saudia Arabia

Wednesday, May 20

IP5Cooperation, Cheating, and Collapse in Biological Populations11:00 AM-11:45 AMRoom:Ballroom

Chair: Jan Medlock, Oregon State University, USA

Natural populations can suffer catastrophic collapse in response to small changes in environmental conditions as a result of a bifurcation in the dynamics of the system. We have used laboratory microbial ecosystems to directly measure theoretically proposed early warning signals of impending population collapse based on critical slowing down. Our experimental yeast populations cooperatively break down sugar, meaning that below a critical size the population cannot sustain itself. The cooperative nature of yeast growth on sucrose makes the population susceptible to “cheater” cells, which do not contribute to the public good and reduce the resilience of the population.

Jeff GoreMassachusetts Institute of Technology, USA



Wednesday, May 20

MS95Control of Multiscale Dynamics - Part II of II1:30 PM-3:30 PMRoom:Magpie B

For Part 1 see MS82 The control of dynamical systems has been extensively studied in the past century, which led to significant applications such as space mission, aerocraft design, or nanoelectromechanical systems. Multiscale simulation and modeling, on the other hand, has become an active field in recent years, due to the multiscale nature of complex systems ubiquitous in practical applications. We consider it an emerging direction to go further and control multiscale systems, which was not possible without contemporary multiscale methods and computational architectures. The proposed minisymposium gathers researchers working on frontiers of related fields, with goals of shaping this new direction and contributing to important applications.

Organizer: Molei TaoGeorgia Institute of Technology, USA

1:30-1:55 Control of a Model of DNA Opening Dynamics via Resonance with a Terahertz FieldWang-Sang Koon, California Institute of

Technology, USA

2:00-2:25 A Dynamical Switching of Reactive and Nonreactive Modes at High EnergiesTamiki Komatsuzaki, Hokkaido University,

Japan; Mikito Toda, Nara Women’s University, Japan; Hiroshi Teramoto, Hokkaido University, Japan

2:30-2:55 Mode-Specific Effects in Structural Transitions of Atomic Clusters with Multiple ChannelsTomohiro Yanao, Waseda University, Japan

3:00-3:25 Obtaining Coarse-Grained Models from Multiscale DataSebastian Krumscheid, École

Polytechnique Fédérale de Lausanne, Switzerland; Greg Pavliotis and Serafim Kalliadasis, Imperial College London, United Kingdom

Wednesday, May 20

MS94First Passage Times in Discrete and Continuous Systems - Part II of II1:30 PM-3:30 PMRoom:Magpie A

For Part 1 see MS81 Numerous problems in nature are formulated in terms of Mean First Passage Time (MFPT) of Brownian particles in the presence of traps. For example, cells are regulated by chemical reactions involving signaling molecules that have to find their targets in a complex and crowded environment. The study of MFPT touches upon many topics and utilizes diverse tools including PDEs, stochastic differential equations, complex variables, generating functions and many others. This mini-session will bring together experts in this active field of research. Directions that will be considered include: search-and-rescue, mobile traps, narrow escape problems on bounded domains, connections to spike solutions of PDEs, and applications in biology and physics.

Organizer: Alan E. LindsayUniversity of Notre Dame, USA

Organizer: Justin C. TzouDalhousie University, Canada

1:30-1:55 Uniform Asymptotic Approximation of Diffusion to a Small TargetJay Newby, The Ohio State University,

USA

2:00-2:25 Narrow Escape to Traps with Absorbing and Reflecting PortionsAlan E. Lindsay, University of Notre

Dame, USA

2:30-2:55 Sampling First-Passage Events When Drift Is Included in the First-Passage Kinetic Monte Carlo MethodAva Mauro, University of Notre Dame,

USA; Samuel A. Isaacson, Boston University, USA

3:00-3:25 Drunken Robber, Tipsy Cop: First Passage Times, Mobile Traps, and Hopf BifurcationsJustin C. Tzou, Shuangquan Xie, and

Theodore Kolokolnikov, Dalhousie University, Canada

Wednesday, May 20

MS93Theoretical Aspects of Spiral and Scroll Wave Dynamics - Part II of II1:30 PM-3:30 PMRoom:Ballroom III

For Part 1 see MS80 Spiral and scroll waves are the most common types of solutions characterizing the dynamics of 2- and 3-dimensional excitable media such as the cardiac tissue. This minisymposium presents a sampling of recent analytical and numerical studies focusing on the interaction of scroll and spiral waves with perturbations such as structural heterogeneities and external stimuli as well as self-interactions and interaction of different spiral/scroll waves with each other.

Organizer: Roman GrigorievGeorgia Institute of Technology, USA

Organizer: Vadim N. BiktashevUniversity of Exeter, United Kingdom

1:30-1:55 Interaction of Electric Field Stimuli with Scroll Waves in Three DimensionsNiels Otani, Rochester Institute of

Technology, USA; Valentin Krinski, CNRS, France

2:00-2:25 Unusually Simple Way to Create Spiral Wave in An Excitable MediumVladimir Zykov, Alexei Krekhov, and

Eberhard Bodenschatz, Max-Planck-Institute for Dynamics and Self-Organization, Germany

2:30-2:55 Describing Scroll Wave Ring Interactions Via Interacting PotentialsFlavio M. Fenton, Georgia Institute of

Technology, USA; Jairo Rodriguez and Daniel Olmos, Universidad de Sonora, Mexico

3:00-3:25 On the Generation of Spiral and Scroll Waves by Periodic Stimulation of Excitable Media in the Presence of Obstacles of Minimum SizeDaniel Olmos and Humberto Ocejo,

Universidad de Sonora, Mexico


Wednesday, May 20

MS99Front Propagation in Advection-Reaction-Diffusion Systems - Part II of II1:30 PM-3:30 PMRoom:Superior A

For Part 1 see MS86 Autocatalytic reactions in a spatially-extended system are characterized by the propagation of reaction fronts separating the species. The front dynamics is generally well-understood for reaction-diffusion systems in the absence of substrate flow. The effects of fluid motion on fronts in the general advection-reaction-diffusion (ARD) case have only recently received significant attention, despite the wide applicability of ARD, including microfluidic chemical reactors, plasmas, ecosystem dynamics in the oceans (e.g., plankton blooms), cellular- and embryonic-scale biological processes. This minisymposium brings together groups studying ARD systems from a variety of perspectives, including experiments, dynamical systems theory, numerical PDEs, and analytics.

Organizer: Kevin A. MitchellUniversity of California, Merced, USA

Organizer: Thomas H. SolomonBucknell University, USA

Organizer: John R. MahoneyUniversity of California, Merced, USA

1:30-1:55 The Domain Dependence of Chemotaxis in a Two-Dimensional Turbulent FlowKimberley Jones and Wenbo Tang, Arizona


2:00-2:25 Flow and Grow: Experimental Studies of Time-Dependent Reaction-Diffusion-Advection SystemsDouglas H. Kelley, University of Rochester,

USA

2:30-2:55 Lagrangian Coherent Structures for Reaction Fronts in Unsteady FlowsKevin A. Mitchell and John R. Mahoney,


3:00-3:25 Transport in Chaotic Fluid ConvectionMark Paul, Virginia Tech, USA

Wednesday, May 20

MS98Advances in Viral Infection Modeling - Part II of II1:30 PM-3:30 PMRoom:Maybird

For Part 1 see MS85 Viral infections, be they acute, like influenza or ebola, or chronic, like HIV, pose a continuing threat to daily life. In recent years mathematical modeling has become an important tool in investigating these infections, and novel methods are rapidly emerging. The primary goal of this minisymposium is to provide a platform for discussion of mathematical advances in viral infection modeling and resulting insights into viral infections, at both the within-host and between-hosts (epidemiological) scales.

Organizer: Jessica M. ConwayPennsylvania State University, USA

Organizer: Naveen K. VaidyaUniversity of Missouri, Kansas City, USA

1:30-1:55 Modeling HCV Infection: Viral Dynamics and Genotypic DiversityRuy M. Ribeiro, Los Alamos National

Laboratory, USA

2:00-2:25 HIV Viral Rebound Times Following Suspension of Art: Stochastic Model PredictionsJessica M. Conway, Pennsylvania State

University, USA

2:30-2:55 Modeling HIV Infection Dynamics under Conditions of Drugs of AbuseNaveen K. Vaidya, University of Missouri,

Kansas City, USA

3:00-3:25 Modeling Equine Infectious Anemia Virus Infection: Virus Dynamics, Immune Control, and EscapeElissa Schwartz, Washington State

University, USA

Wednesday, May 20

MS96Wave Propagation in Highly Nonlinear Dispersive Media - Part II of II1:30 PM-3:30 PMRoom:Wasatch A

For Part 1 see MS83 Wave propagation in highly nonlinear dispersive media has recently attracted considerable attention of the interdisciplinary community that includes applied mathematicians, physicists and engineers. In particular, dynamics of granular crystals has been a subject of intensive theoretical and experimental research because of their unique, adaptive dynamical properties. Strongly nonlinear dispersive media may exhibit quite intriguing phenomena such as broadband absorption, high-rate wave attenuation and strong energy localization, rendering them highly attractive for multiple engineering applications. In this minisymposium, leading experts dealing with this class of dynamical systems will come together for a creative exchange of ideas involving fundamental and applied research.

Organizer: Anna VainchteinUniversity of Pittsburgh, USA

Organizer: Yuli StarosvetskyTechnion - Israel Institute of Technology, Israel

1:30-1:55 Nonlinear Dynamics of Non-Stretched MembraneLeonid Manevich, Russian Academy of

Sciences, Russia

2:00-2:25 Discrete Breathers in Vibro-Impact Lattice ModelsItay Grinberg and Oleg Gendelman,

Technion Israel Institute of Technology, Israel

2:30-2:55 Mixed Solitary – Shear Waves in a Granular NetworkYijing Zhang, University of Illinois at

Urbana-Champaign, USA; Md. Arif Hasan, University of Illinois, USA; Yuli Starosvetsky, Technion - Israel Institute of Technology, Israel; D. Michael McFarland and Alexander Vakakis, University of Illinois, USA

3:00-3:25 Stable Two-Dimensional Solitons in Free Space: Gross-Pitaevskii Equations with the Spin-Orbit CouplingBoris Malomed, Tel Aviv University, Israel


Wednesday, May 20

MS102Complex Network Theory Based Approaches in the Analyses of Complex Systems and Data - Part II of II1:30 PM-3:00 PMRoom:Primrose A

For Part 1 see MS89 Analysis of network data obtained from a complex system is often a challenging task. In this minisymposium we will be discussing few novel approaches for obtaining insights into the structural and functional properties of empirical networks and networks inferred from data. One of our focus areas will be to employ simulation of variety of dynamical processes on networks to study properties of empirical networks. We will also discuss methodologies to overcome problems in the analysis of empirical networks due to spurious or missing links. Dynamical system based approaches for transforming data into a network representing will also be presented.

Organizer: Nishant MalikUniversity of North Carolina at Chapel Hill, USA

1:30-1:55 Shadow Networks: Discovering Hidden Nodes with Models of Information FlowJames Bagrow, University of Vermont,

USA

2:00-2:25 A Network Measure for the Analysis and Visualization of Large-Scale GraphsRoldan Pozo, National Institute of

Standards and Technology, USA

2:30-2:55 Revealing Collectivity in Evolving Networks: A Random Matrix Theory ApproachSaray Shai, University of North Carolina at

Chapel Hill, USA

Wednesday, May 20

MS101Models from Data1:30 PM-3:30 PMRoom:White Pine

Data modeling uses a model to represent a possibly large data set with a much smaller set of rules. The type of model depends on the goal of the modeling; data assimilation techniques can be used to create predictive models. If one wants to discover the structure of the data set, manifold learning techniques can reveal that a data set that appears high dimensional actually exists on a low dimensional manifold. Both types of modeling seek simple descriptions of complicated data sets.

Organizer: Thomas L. CarrollNaval Research Laboratory, USA

1:30-1:55 Nonlinear Dynamics of Variational Data AssimilationHenry D. Abarbanel, Kadakia Nirag,

Jingxin Ye, Uriel I. Morone, and Daniel Rey, University of California, San Diego, USA

2:00-2:25 Precision Variational Approximations in Statistical Data AssimilationJingxin Ye, University of California, San

Diego, USA

2:30-2:55 Manifold Learning Approach for Modelling Collective Chaos in High-Dimensional Dynamical SystemsHiromichi Suetani, Kagoshima University,

Japan

3:00-3:25 Attractor Comparisons Based on DensityThomas L. Carroll, Naval Research

Laboratory, USA

Wednesday, May 20

MS100Nonsmooth Dynamical Systems: Theory and Applications - Part II of II1:30 PM-3:30 PMRoom:Superior B

For Part 1 see MS87 Many physical systems involve abrupt events, such as switches, impacts or thresholds, and are well-modelled by equations that are nonsmooth. This minisymposium will discuss novel applications of nonsmooth systems in ecology, optics and neuroscience, as well as describe new developments in the theory of nonsmooth systems. Overall the talks will highlight the various nuances of nonsmooth systems and show how these relate to the dynamical behaviour of the physical systems being modelled.

Organizer: David J. SimpsonMassey University, New Zealand

1:30-1:55 Lost in Transition: Nonlinearities in the Dynamics of SwitchingMike R. Jeffrey, University of Bristol,

United Kingdom

2:00-2:25 Some Nonsmooth Problems Inspired by Conceptual Climate ModelsAnna M. Barry, University of British

Columbia, Canada

2:30-2:55 Grazing Bifurcations in Engineering and Medical SystemsMarian Wiercigroch, University of

Aberdeen, United Kingdom

3:00-3:25 Continuation of Chatter in a Mechanical ValveHarry Dankowicz and Erika Fotsch,

University of Illinois at Urbana-Champaign, USA; Alan R. Champneys, University of Bristol, United Kingdom


Wednesday, May 20

MT2Stochastic Dynamics of Rare Events4:00 PM-6:00 PMRoom:Ballroom III

Chair: Eric Forgoston, Montclair State University, USA

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. The noise may be internal or external - internal noise is inherent to the system itself and arises due to the random interactions of a finite number of agents in the system, while external noise arises from a source outside of the system. In recent years, researchers have identified situations where even weak noise can induce a large fluctuation that leads to population extinction, switching between metastable states in ecological systems, or the escape of a particle from a potential well. The purpose of this minitutorial is to expose the audience to the theory underlying the dynamics of rare events for stochastic ODEs and PDEs along with a wide variety of applications.

Noise-Induced Rare Events: Switching, Escape, and Extinction in Stochastic ODEsEric Forgoston, Montclair State University,

USA

Noise-Induced Rare Events: Failures and Exits in Stochastic Wave EquationsRichard O. Moore, New Jersey Institute of

Technology, USA

Noise-Induced Rare Events: Applications in Physical and Biological SciencesMichael Khasin, NASA Ames Research

Center, USA

Wednesday, May 20

MS119From Singular Perturbation Theory to some Slow-Fast Systems: A Taste1:30 PM-3:30 PMRoom:Wasatch B

Geometric Singular Perturbation Theory and the rôle of an small parameter in Fast-Slow systems permit to decompose the dynamics and to analyse global changes and bifurcations when such parameter decreases. Besides, Singular Perturbation Theory is closely related to problems concerning persistence of homo/heteroclinic connections, beyond-all-orders algebraic expansions and Stokes phenomenon. The aim of this minisymposium is to offer a very general (but partial) overview of some of these problems under both a theoretical and numerical viewpoints.

Organizer: J. Tomas LazaroUniversitat Politecnica de Catalunya, Spain

Organizer: Sergio SerranoUniversity of Zaragoza, Spain

1:30-1:55 Stokes Phenomenon in a Singularly Perturbed Differential EquationVassili Gelfreich, University of Warwick,

United Kingdom

2:00-2:25 Homoclinic Orbits With Many Loops Near a 02 iΏ Resonant Fixed Point Of Hamiltonian SystemsTiphaine Jézéquel, University of Tours,

France; Patrick Bernard, CEREMADE Universite Paris 9 Dauphine, France; Éric Lombardi, Universite Paul Sabatier, France

2:30-2:55 Canard Orbits and Mixed-Mode Oscillations in a Chemical Reaction ModelBernd Krauskopf, Jose Mujica, and Hinke

M. Osinga, University of Auckland, New Zealand

3:00-3:25 Symbolic Dynamical Unfolding of Spike-Adding Bifurcations in Chaotic Neuron ModelsRoberto Barrio, University of Zaragoza,

Spain; Marc Lefranc, PHLAM - Universite de Lille, France; M. Angeles Martinez and Sergio Serrano, University of Zaragoza, Spain


Wednesday, May 20

MS103Transfer Operator Methods: Geometry, Continuous Time, Infinite Dimensions, Fast Computation1:30 PM-3:30 PMRoom:Primrose B

Transfer operators are global descriptors of ensemble evolution under nonlinear dynamics and efficient methods of computing coherent structures and attractors. The speakers will describe advances in four areas. First, a new fundamental geometric characterisation of finite-time coherent sets and its associated transfer operator. Second, new spectral theory and numerics for periodically-driven flows and their time-asymptotic coherent sets. Third, a transfer operator approach to computing attractors for infinite-dimensional delay differential equations. Fourth, numerical methods for computing coherent sets for time-dependent advection-diffusion equations.

Organizer: Gary FroylandUniversity of New South Wales, Australia

Organizer: Kathrin Padberg-GehleDresden University of Technology, Germany

1:30-1:55 The Geometry of Lagrangian Coherent StructuresGary Froyland, University of New South

Wales, Australia

2:00-2:25 Coherent Families: Spectral Theory for Transfer Operators in Continuous TimePeter Koltai, Free University of Berlin,

Germany; Gary Froyland, University of New South Wales, Australia

2:30-2:55 On the Computation of Attractors for Delay Differential EquationsMichael Dellnitz, University of Paderborn,

Germany

3:00-3:25 Computing Coherent Sets in Turbulent SystemsAndreas Denner, Technische Universitaet

Muenchen, Germany; Oliver Junge, University of Paderborn, Germany


Wednesday, May 20

MS106Featured Minisymposium: Time-Delayed Feedback4:00 PM-6:00 PMRoom:Wasatch B

Time-delayed feedback is a simple and powerful method for influencing and controlling complex nonlinear systems. In its simplest form, the method has been successfully used to control unstable periodic orbits in dynamical models arising for instance in engineering, physics or biology. More recently, the scope of time-delayed feedback has been expanded to systems with multiple delay and the connection with fixed point problems has been clarified. In this minisymposium we will cover these new developments and discuss applications of time delay to climate systems and cluster synchronisation

Organizer: Andreas AmannUniversity College Cork, Ireland

4:00-4:25 Pattern Formation in Systems with Multiple Delayed FeedbacksSerhiy Yanchuk, Humboldt University at

Berlin, Germany

4:30-4:55 Connection Between Extended Time-Delayed Feedback and Nonlinear Fixed-Point ProblemsJan Sieber, University of Exeter, United

Kingdom

5:00-5:25 Interplay of Adaptive Topology and Time Delay in the Control of Cluster SynchronizationJudith Lehnert, Technische Universität

Berlin, Germany; Alexander Fradkov, St. Petersburg State University, Russia; Eckehard Schöll and Philipp Hövel, Technische Universität Berlin, Germany; Anton Selivanov, St. Petersburg State University, Russia

5:30-5:55 Bifurcation Analysis of a Model for the El Nño Southern OscillationAndrew Keane, Bernd Krauskopf, and

Claire Postlethwaite, University of Auckland, New Zealand

Wednesday, May 20

MS105Featured Minisymposium: Random Walks, First Passage Time and Applications4:00 PM-6:00 PMRoom:Ballroom II

Numerous problems -- from the molecular to macroscopic scales -- involve strategies based on random (possibly biased) walks. Examples range from fast-folding DNA strands, to predator-prey interactions and search and rescue operations. In this featured symposium, we present novel results in the field that also show the diversity and beauty of the subject. The proposed speakers are world-renowned experts that will present new applications to problems in cellular biology, chemistry, statistical mechanics, neuroscience and even sports. The topics of this session unify various approaches used, offering unique perspectives to reach and inform a wide target audience.

Organizer: Theodore KolokolnikovDalhousie University, Canada

Organizer: Sidney RednerSanta Fe Institute, USA

4:00-4:25 First Passage Time Problems for Stochastic Hybrid SystemsPaul C. Bressloff, University of Utah, USA

and University of Oxford, United Kingdom

4:30-4:55 Exploration and Trapping of Mortal Random WalkersKatja Lindenberg, University of

California, San Diego, USA; Santos B. Yuste and Enrique Abad, Universidad de Extremadura, Spain

5:00-5:25 Trajectory-to-Trajectory Fluctuations in the First-Passage Phenomena in Bounded DomainsGleb Oshanin, Laboratoire de Physique

Théorique de la Matière Condensée, France

5:30-5:55 Application of First-Passage Ideas to the Statistics of Lead Changes in BasketballSidney Redner, Santa Fe Institute, USA;

Aaron Clauset, University of Colorado Boulder, USA; Marina Kogan, University of Colorado, USA

Wednesday, May 20

MS104Featured Minisymposium: Non-Autonomous Instabilities4:00 PM-6:00 PMRoom:Ballroom I

In many applications from the natural sciences and engineering aperiodic external forcing often leads to interesting nonlinear phenomena that can be characterised as non-autonomous instabilities. Such instabilities are mathematically challenging and often puzzle scientists because they cannot, owing to their transient or finite-time nature, be explained using traditional bifurcation theory. This minisymposium highlights recent techniques to analyse stability of non-autonomous ODEs and PDEs, with applications to rate-induced tipping points, failure boundaries in earthquake engineering and finite-time transport in (ocean) surface flows.

Organizer: Sebastian M. WieczorekUniversity College Cork, Ireland

4:00-4:25 Rate-Induced Bifurcations in Slow-Fast SystemsSebastian M. Wieczorek, University

College Cork, Ireland

4:30-4:55 Interactions Between Noise and Rate-Induced TippingPaul Ritchie, University of Exeter, United

Kingdom

5:00-5:25 A Direct Method for Computing Failure Boundaries of Non-autonomous SystemsHinke M. Osinga, University of Auckland,

New Zealand

5:30-5:55 Finite-Time Lagrangian Transport Through Surfaces in Volume-Preserving FlowsDaniel Karrasch, ETH Zürich, Switzerland


Wednesday, May 20

MS109Featured Minisymposium: Medical Applications4:00 PM-6:00 PMRoom:Primrose B

In recent years, there has been growing interest in employing ideas from dynamical systems and control theory for medical applications. This minisymposium will emphasize recent theoretical and experimental advances in the way such approaches may be used to both understand and combat the underlying mechanisms of dysfunction that can occur for specific diseases. We include a broad sampling of speakers representing applications from the fields of cardiology, neuroscience, and diabetes research.

Organizer: Dan D. WilsonUniversity of California, Santa Barbara, USA

Organizer: Jeff MoehlisUniversity of California, Santa Barbara, USA

4:00-4:25 Termination of Cardiac Alternans Using Isostable Response CurvesDan D. Wilson and Jeff Moehlis, University

of California, Santa Barbara, USA

4:30-4:55 Unification of Neuronal Spikes, Seizures, and Spreading DepressionSteven J. Schiff, Pennsylvania State

University, USA; Yina Wei, University of California, Riverside, USA; Ghanim Ullah, University of South Florida, USA

5:00-5:25 Therapeutic Mechanisms of High Frequency DBS in Parkinson’s Disease: Neural Restoration Through Loop-Based ReinforcementSridevi Sarma, Johns Hopkins University,

USA; Sabato Santaniello, University of Colorado Boulder, USA

5:30-5:55 Perspectives on Theories of Diabetogenesis and Glucose ManagementPranay Goel, Indian Institute for Science

Education and Research, Pune, India; Saroj Ghaskadbi, Savitribai Phule Pune University, India


Wednesday, May 20

MS108Featured Minisymposium: Invariant Manifolds Unravelling Complicated Dynamics4:00 PM-6:00 PMRoom:Primrose A

Global invariant manifolds of maps and vector fields undergo critical re-arrangements under parameter variation. These topological and geometric transitions may result in drastic changes of the global dynamics. Typically, major changes to invariant manifolds may trigger the onset of chaos, transformation or creation of basins of attraction, the formation of homo- and heteroclinic orbits and, ultimately, the reorganization of the overall structure of the phase space. The aim of this minisymposium is to present recent advances and discuss new challenges in the way invariant manifolds can be used as a tool to understand complicated global phenomena.

Organizer: Stefanie HittmeyerUniversity of Auckland, New Zealand

Organizer: Pablo AguirreUniversidad Técnica Federico Santa María, Chile

4:00-4:25 Bifurcations of Generalised Julia Sets Near the Complex Quadratic FamilyStefanie Hittmeyer, Bernd Krauskopf, and

Hinke M. Osinga, University of Auckland, New Zealand

4:30-4:55 Parameterization Method for Local Stable/unstable Manifolds of Periodic OrbitsJason Mireles James, Rutgers University,

USA

5:00-5:25 A Global Bifurcation of Mixed-mode OscillationsIan M. Lizarraga and John Guckenheimer,

Cornell University, USA

5:30-5:55 Practical Stability Versus Diffusion in the Spatial Restricted Three-body ProblemMaisa O. Terra, Technological Institute

of Aeronautics, Brazil; Carles Simó, University of Barcelona, Spain; Priscilla de Sousa-Silva, Technological Institute of Aeronautics, Brazil

Wednesday, May 20

MS107Featured Minisymposium: Emerging Strategies for Stability Analysis of Electrical Power Grids4:00 PM-6:00 PMRoom:Maybird

The so-called swing equations which describe the course grained dynamics on an electrical power grid are highly non-linear with a solution space that grows with the size of the grid. Due to their rich dynamics, the equations have been the subject of intense research using a wide range of techniques. This minisymposium focuses on the global structure of these equations and develops new approaches to study the system stability by using a combination of tools such as power flow approximations, bifurcation theory, Lyapunov functions and stochastic methods. The speakers will discuss their latest results in this area and present examples of relevance in applications.

Organizer: Lewis G. RobertsUniversity of Bristol, United Kingdom

Organizer: Florian DorflerETH Zürich, Switzerland

4:00-4:25 A Parametric Investigation of Rotor Angle Stability Using Direct MethodsLewis G. Roberts, Alan R. Champneys, and

Mario Di Bernardo, University of Bristol, United Kingdom; Keith Bell, University of Strathclyde, United Kingdom

4:30-4:55 Voltage Stability in Power Networks and MicrogridsFlorian Dorfler, ETH Zürich, Switzerland;

John Simpson-Porco, University of California, USA; Francesco Bullo, University of California, Santa Barbara, USA

5:00-5:25 Finding Useful Statistical Indicators of Instability in Stochastically Forced Power SystemsGoodarz Ghanavati, Paul Hines, and Taras

Lakoba, University of Vermont, USA

5:30-5:55 Synchronization Stability of Lossy and Uncertain Power GridsKonstantin Turitsyn and Thanh Long Vu,



Feasibility of Binding Heteroclinic NetworksXue Gong, Ohio University, USA; Valentin

Afraimovich, Universidad Autonoma de San Luis Potosi, Mexico

Dynamic Square Patterns in 2D Neural FieldsKevin R. Green and Lennaert van Veen,

University of Ontario Institute of Technology, Canada

Controllability of Brain NetworksShi Gu, University of Pennsylvania, USA;

Fabio Pasqualetti, University of California, Riverside, USA; Matthew Ceislak and Scott Grafton, University of California, Santa Barbara, USA; Danielle S. Bassett, University of Pennsylvania, USA

Compressive Sensing with Exactly Solvable ChaosSidni Hale, Anthony DiPofi, and Bradley

Kimbrell, Radix Phi, USA

Identifying the Role of Store-Operated Calcium Channels in Astrocytes Via An Open-Cell ModelGregory A. Handy, Alla Borisyuk, Marsa

Taheri, and John White, University of Utah, USA

Behavioral Dynamics and STD TransmissionMichael A. Hayashi and Marisa Eisenberg,

University of Michigan, USA

Master Stability Functions for the Fixed Point Solution of Synchronized Identical Systems with Linear Delay-Coupling and a Single Constant DelayStanley R. Huddy and Jie Sun, Clarkson

University, USA

Windows of Opportunity: Synchronization in On-Off Stochastic NetworksRussell Jeter and Igor Belykh, Georgia State

University, USA

Two-Theta Neuron: Phase Models for Bursting NetworksAaron Kelley, Georgia State University, USA

Canard-Mediated Dynamics in a Phantom BursterElif Köksal Ersöz, Mathieu Desroches,

Maciej Krupa, and Frédérique Cleément, INRIA Paris-Rocquencourt, France

A Mathematical Model for Adaptive Crawling LocomotionShigeru Kuroda and Toshiyuki Nakagaki,

Hokkaido University, Japan

Slow-fast Analysis of Earthquake FaultingElena Bossolini, Kristian Uldall

Kristiansen, and Morten Brøns, Technical University of Denmark, Denmark

Quasicycles in the Stochastic Hybrid Morris-Lecar Neural ModelHeather A. Brooks, University of Utah,

USA; Paul C. Bressloff, University of Utah, USA and University of Oxford, United Kingdom

Computation of Normally Hyperbolic Invariant ManifoldsMarta Canadell, Georgia Institute of

Technology, USA; Alex Haro, Universitat de Barcelona, Spain

A Novel Speech-Based Diagnostic Test for Parkinson’s Disease Integrating Machine Learning with Web and Mobile Application Development for Cloud DeploymentPooja Chandrashekar, Thomas Jefferson

High School of Science and Techonology, USA

An Agent-Based Model for mRNA Localization in Frog OocytesVeronica M. Ciocanel and Bjorn


Effects of Stochastic Gap-Junctional Coupling in Cardiac Cells and TissueWilliam Consagra, Rochester Institute of

Technology, USA

Maximizing Plant Fitness Under Herbivore AttackKaren M. Cumings, Peter R. Kramer, and

Bradford C. Lister, Rensselaer Polytechnic Institute, USA

The Derivation of Mass Action Laws: Issues and QuestionsJonathan Dawes, University of Bath,

United Kingdom; Max O. Souza, Universidade Federal Fluminense, Brazil

Heterogeneity and Oscillations in Small Predator-Prey SwarmsJeff Dunworth and Bard Ermentrout,


Bacterial Disinfection with the Presence of PersistersSepideh Ebadi, Florida State University,

USA

Chaotic Mixing in a Curved Channel with Slip SurfacesPiyush Garg, Indian Institute of

Technology Roorkee, India; Jason R. Picardo and Subramaniam Pushpavanam, Indian Institute of Technology Madras, India

Wednesday, May 20


Intermittent Synchronization/desynchronization in Population DynamicsSungwoo Ahn, Arizona State University,

USA; Leonid Rubchinsky, Indiana University - Purdue University Indianapolis, USA

Parabolic Bursting in Inhibitory Neural CircuitsDeniz Alacam and Andrey Shilnikov,

Georgia State University, USA

An Accurate Computation of the Tangent Map for Computation of Lagrangian Coherent StructuresSiavash Ameli and Shawn Shadden,

University of California, Berkeley, USA

Nonlinear Dynamics in Coupled Semiconductor Laser Network ImplementationsApostolos Argyris, Michail Bourmpos,

Alexandros Fragkos, and Dimitris Syvridis, National & Kapodistrian University of Athens, Greece

Symplectic Maps with Reversed Current in a TokamaksBruno Bartoloni and Ibere L. Caldas,

University of Sao Paulo, Brazil

Analysis of Spatiotemporal Dynamical Systems from Multi-Attribute Satellite ImagesRanil Basnayake and Erik Bollt, Clarkson

University, USA; Nicholas Tufillaro, Oregon State University, USA; Jie Sun, Clarkson University, USA

Phase Response Analysis of the Circadian Clock in Neurospora CrassaJacob Bellman, University of Cincinnati,

USA

Time Series Based Prediction of Extreme Events in High-Dimensional Excitable SystemsStephan Bialonski, Max Planck Institute

for Dynamics of Complex Systems, Germany; Gerrit Ansmann, University of Bonn, Germany; Holger Kantz, Max Planck Institute for Physics of Complex Systems, Germany

continued on next pagecontinued in next column continued in next column


Osteocyte Network FormationJake P. Taylor-King, Mason A. Porter,

and Jon Chapman, University of Oxford, United Kingdom; David Basanta, H. Lee Moffitt Cancer Center & Research Institute, USA

On a FitzHugh-Nagumo Kinetic Model for Neural NetworksCristobal Quininao, Laboratoire Jacques-

Louis Lions, France; Jonathan D. Touboul, Collège de France, France; Stéphane Mischler, Universite Paris 9 Dauphine, France

Examining Partial Cascades in Clustered Networks with High Intervertex Path LengthsYosef M. Treitman and Peter R. Kramer,

Rensselaer Polytechnic Institute, USA

Almost Complete Separation of a Fluid Component from a Mixture Using the Burgers Networks of Micro-separatorsShinya Watanabe, Ibaraki University,

Japan; Sohei Matsumoto, National Institute of Advanced Industrial Science and Technology, Japan; Tomohiro Higurashi, Yuya Yoshikawa, and Naoki Ono, Shibaura Institute of Technology, Japan

New Data Anysis Approach for Complex Signals with Low Signal to Noise Ratio’sJeremy Wojcik, Georgia State University,

USA

Data Assimilation for Traffic State and Parameter EstimationChao Xia, Bjorn Sandstede, and Paul

Carter, Brown University, USA; Laura Slivinski, Woods Hole Oceanographic Institute, USA

Stochastic Active-Transport Model of Cell PolarizationBin Xu, University of Utah, USA; Paul C.

Bressloff, University of Utah, USA and University of Oxford, United Kingdom

Statistical Properties of Finite Systems of Point-Particles Interacting Through Binary CollisionsAlexander L. Young, Joceline Lega,

and Sunder Sethuraman, University of Arizona, USA

Capacity for Learning the Shape of Arena in the Single-Celled Swimmer, Viewed from Slow Dynamics of Membrane PotentialToshiyuki Nakagaki and Itsuki Kunita,

Hokkaido University, Japan; Tatsuya Yamaguchi, Kyushu University, Japan; Masakazu Akiyama, Hokkaido University, Japan; Atsushi Tero, Kyushu University, Japan; Shigeru Kuroda and Kaito Ooki, Hokkaido University, Japan

Co-Dimension Two Bifurcations in Piecewise-Smooth Continuous Dynamical SystemsWilten Nicola and Sue Ann Campbell,

University of Waterloo, Canada

Analysis of Malaria Transmission Dynamics with Saturated IncidenceSamson Olaniyi, Ladoke Akintola

University of Technology, Nigeria

Temporally Periodic Neural Responses from Spatially Periodic StimuliJason E. Pina and Bard Ermentrout,


Using a Stochastic Field Theory to Understand Collective Behavior of Swimming MicroorganismsYuzhou Qian, Peter R. Kramer, and

Patrick Underhill, Rensselaer Polytechnic Institute, USA

Consensus and Synchronization over Biologically-Inspired Networks: From Collaboration to AntagonismSubhradeep Roy and Nicole Abaid,

Virginia Tech, USA

Oscillatory Shear Flow Influence on the Two Point Vortex DynamicsEvgeny Ryzhov and Konstantin Koshel,

Pacific Oceanological Institute of the Russian Academy of Sciences, Russia

Wild Dynamics in Nonlinear Integrate-and-Fire Neurons: Mixed-Mode Bursting, Spike Adding and ChaosJustyna H. Signerska, INRIA, France;

Jonathan D. Touboul, Collège de France, France; Alexandre Vidal, University of Evry-Val-d’Essonne, France

Return Times and Correlation Decay in Linked Twist MapsRob Sturman, University of Leeds, United

Kingdom

Wednesday, May 20


cont.

Effective Dispersion Relation of the Nonlinear Schrödinger EquationKatelyn J. Leisman and Gregor Kovacic,

Rensselaer Polytechnic Institute, USA; David Cai, Courant Institute of Mathematical Sciences, New York University, USA

Mathematical Model of Bidirectional Vesicle Transport and Sporadic Capture in AxonsEthan Levien, University of Utah, USA;

Paul C. Bressloff, University of Utah, USA and University of Oxford, United Kingdom

Modelocking in Chaotic Advection-Reaction-Diffusion SystemsRory A. Locke, John R. Mahoney,

and Kevin A. Mitchell, University of California, Merced, USA

Effect of Multi-Species Mass Emergence on BiodiversityJames E. McClure and Nicole Abaid,

Virginia Tech, USA

A B Cell Receptor Signaling Model and Dynamic Origins of Cell ResponseReginald Mcgee, Purdue University, USA

Stability of Morphodynamic Equilibria in Tidal BasinsCorine J. Meerman and Vivi Rottschäfer,

Leiden University, Netherlands; Henk Schuttelaars, Delft University of Technology, Netherlands

Frequency-Dependent Left-Right Coordination in Locomotor Pattern GenerationYaroslav Molkov, Indiana University -

Purdue University Indianapolis, USA; Bartholomew Bacak, Drexel University College of Medicine, USA; Ilya A. Rybak, Drexel University, USA

continued in next column continued in next columncontinued on next page

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Thursday, May 21

MS111Recent Insights into Controling Flow Structures - Part I of II8:30 AM-10:30 AMRoom:Ballroom II

For Part 2 see MS124 Interior flow entities such as fluid interfaces, coherent structures and invariant manifolds have a profound influence on transport in unsteady flows. The ability to control them is attracting much recent interest, fueled in part by emerging biotechnological applications at the microfluidic level. This minisymposium will cover a range of state-of-the-art approaches to controling flow structures which are inspired by dynamical systems methods.

Organizer: Sanjeeva BalasuriyaUniversity of Adelaide, Australia

Organizer: Marko BudisicUniversity of Wisconsin, Madison, USA

Organizer: Jean-Luc ThiffeaultUniversity of Wisconsin, Madison, USA

8:30-8:55 Control of Thin-Layer Flows with Patterned SurfacesJean-Luc Thiffeault, University of

Wisconsin, Madison, USA; Jay Johnson, University of Texas at Austin, USA

9:00-9:25 Mesohyperbolicity, Mix-Norm and the Hunt for Mh370Sophie Loire and Hassan Arbabi, University

of California, Santa Barbara, USA; Stefan Ivic, Rijeka University, Croatia; Patrick Clary, University of California, Santa Barbara, USA; Bojan Crnkovic and Nelida Crnjaric-Zic, Rijeka University, Croatia; Igor Mezic, University of California, Santa Barbara, USA

Thursday, May 21


MS110Effective Multiscale Computational Modeling of Spatio-temporal Systems8:30 AM-10:30 AMRoom:Ballroom I

Across science and engineering many systems are only realistically described by models on multiple spatial and temporal scales. Such multiscale systems are notoriously complex and computationally demanding. In developing the desired ‘coarse-grained’ or macroscale model, major concerns are the efficiency of the the macroscale modelling and its accuracy. We discuss recent developments in the computational modelling of the emergent dynamics of multiscale systems.

Organizer: Anthony J. RobertsUniversity of Adelaide, Australia

8:30-8:55 Better Buffers for Patches in Macroscale Simulation of Systems with Microscale RandomnessAnthony J. Roberts, University of

Adelaide, Australia

9:00-9:25 Resilient Algorithms for Reconstructing and Simulating Gappy Flow Fields in CFDSeungjoon Lee, Brown University, USA;

Ioannis Kevrekedis, Princeton University, USA; George E. Karniadakis, Brown University, USA

9:30-9:55 Triggers of Rogue Waves in Deep Water Envelope EquationsWill Cousins and Themistoklis Sapsis,


10:00-10:25 Boundary Conditions and the Linking of Computational Domains in Patch Dynamics SchemesI. G. Kevrekidis, Princeton University,

USA

Heteroclinic Separators of Magnetic Fields in Electrically Conducting FluidsEvgeny Zhuzhoma, National Research

University Higher School of Economics, Russia; Vyatcheslav Grines and Timur Medvedev, Lobachevsky State University of Nizhny Novgorod, Russia; Olga Pochinka, National Research University Higher School of Economics, Russia

Equivalent Probability Density Moments Determine Equivalent Epidemics in An Sirs Model with Temporary ImmunityThomas W. Carr, Southern Methodist

University, USA

Waveaction Spectra for Fully Nonlinear MMT ModelMichael Schwarz, Gregor Kovacic, and

Peter R. Kramer, Rensselaer Polytechnic Institute, USA; David Cai, Shanghai Jiao Tong University, China and Courant Institute of Mathematical Sciences, New York University, USA

Rigorous Numerics for Analytic Solutions of Differential Equations: The Radii Polynomial ApproachAllan R. Hungria, University of Delaware,

USA; Jean-Philippe Lessard, Université Laval, Canada; Jason Mireles-James, Florida Atlantic University, USA



Thursday, May 21

MS113Statistical Physics and Nonlinear Dynamics for the Earth’s Cryosphere8:30 AM-10:30 AMRoom:Magpie A

Important elements of the Earth’s Cryosphere such as sea ice, permafrost and snow were formed under temperature change resulting in nonlinear phase transitions. These critical phenomena in the Earth’s Cryosphere remain of continuing interest as the climate system warms, and are crucial for the stability of the climate system. The melting processes in the Earth’s Cryosphere can be investigated through classical statistical physics models as well the nonlinear behaviour of the climate system caused by phase transitions can be described with help of standard nonlinear dynamics tools.

Organizer: Ivan SudakovUniversity of Utah, USA

8:30-8:55 Statistical Physics Models for Critical Phenomena in Permafrost LakesIvan Sudakov, University of Utah, USA

9:00-9:25 The Evolution of Complexity in Arctic Melt Ponds: a Statistical Physics PerspectiveYiping Ma, University of Colorado Boulder,

USA

9:30-9:55 How Climate Model Complexity Impacts the Stability of the Sea Ice CoverTill Wagner, University of California,

San Diego, USA; Ian Eisenman, Scripps Institution of Oceanography, USA

10:00-10:25 Growth and Fluctuations of Suncups on Alpine Snowpacks: Comparison of Field Observations with a Nonlinear Pde ModelTom Tiedje, University of Victoria,

Canada; Kevin A. Mitchell, Simon Fraser University, Canada

Thursday, May 21

MS112Dynamical Systems Aspects of Legged Locomotion8:30 AM-10:30 AMRoom:Ballroom III

The purpose of this minisymposium is to review the state of the art in biomechanical and neural modelling of legged locomotion. Topics covered will include interaction between central pattern generators and muscles, experimental observation of human subjects on steady and moving ground, cross-species comparison, stability, basins of attraction, gait transition, feedback control and reduced-order models.

Organizer: Shinya AoiKyoto University, Japan

Organizer: Alan R. ChampneysUniversity of Bristol, United Kingdom

8:30-8:55 What Can Coupled, Nonlinear Oscillators Say About Noisy, Perturbed CockroachesPhilip Holmes, Princeton University, USA

9:00-9:25 Formation Mechanism for Basin of Attraction of Bipedal Working ModelsObayashi Ippei, Kyoto University, Japan

9:30-9:55 Experimental Observation of Rhythm Control of Human Gait Using Moving FloorTetsuro Funato, University of Electro-

Communications, Japan; Shinya Aoi, Nozomi Tomita, and Tsuchiya Kazuo, Kyoto University, Japan

10:00-10:25 Lateral Balance of Human Walking and Human Structure InteractionJohn Macdonald, Jeremy Burn, Matteusz

Bocian, and Alan R. Champneys, University of Bristol, United Kingdom

Thursday, May 21

MS111Recent Insights into Controling Flow Structures - Part I of II8:30 AM-10:30 AMRoom:Ballroom II

cont.

9:30-9:55 Closed-Loop Control of Complex and Turbulent Flows Using Machine Learning Control: a Reverse Engineering ApproachThomas Duriez, Buenos Aires University,

Argentina; Vladimir Parezanovic, Kai Von Krbek, Jean-Paul Bonnet, Laurent Cordier, and Bernd R. Noack, CNRS, France; Marc Segond and Markus W Abel, Ambrosys GmbH, Germany; Nicolas Gautier and Jean-Luc Aider, CNRS, France; Cedric Raibaudo, Christophe Cuvier, and Michel Stanislas, École Centrale de Lille, France; Antoine Debien, Nicolas Mazellier, and Azeddine Kourta, Universite d’Orleans, France; Steven Brunton, University of Washington, USA

10:00-10:25 Controlling Hyperbolic Trajectories and Invariant Manifolds in FlowsSanjeeva Balasuriya, University of

Adelaide, Australia; Kathrin Padberg-Gehle, Dresden University of Technology, Germany


Thursday, May 21

MS117Complex Collective Dynamics of Oscillator Networks - Part I of II8:30 AM-10:30 AMRoom:Maybird

For Part 2 see MS129 Considerable progress has recently been made in understanding the collective dynamics of large oscillator networks. New analytical tools have been created and extended in their applicability, and novel effects have been demonstrated not only theoretically and numerically, but also experimentally. Results in this field have broad application to both physical and biological systems. Part one of this symposium will report recent general mean field results involving chimera states, assortative networks, and generalizations of the classic Kuramoto model. Part two will focus on networks of neuronal oscillators, their relationship to field models, and the dynamical consequences of connectivity.

Organizer: Paul SoGeorge Mason University, USA

Organizer: Arkady PikovskyUniversity of Potsdam, Germany

Organizer: Ernest BarretoGeorge Mason University, USA

8:30-8:55 Chimera States in Globally Coupled OscillatorsArkady Pikovsky, Michael Rosenblum, and

Azamat Yeldesbay, University of Potsdam, Germany

9:00-9:25 On the Mechanical Origin of Chimera StatesErik A. Martens, University of

Copenhagen, Denmark

9:30-9:55 The Kuramoto Model of Coupled Oscillators with a Bi-Harmonic Coupling FunctionMaxim Komarov, Potsdam University, Germany10:00-10:25 Mean Field Theory of Assortative Networks of Phase OscillatorsJuan G. Restrepo, University of Colorado

Boulder, USA; Edward Ott, University of Maryland, USA

Thursday, May 21

MS115Inverse Problems in Network Dynamics - Part I of II8:30 AM-10:30 AMRoom:Wasatch A

For Part 2 see MS127 Network Dynamics constitutes a rapidly expanding field with applications in natural and social science, medicine, engineering, and beyond. Commonly, mathematical scientists study how a specific network model behaves collectively as a function of parameters or inputs. Here, taking a complementary view, we ask what recorded time series from a network’s units and respective correlation and information measures tell us about the units’ local dynamics and their real physical interactions. Such inverse network dynamics are much less explored and even less understood. The minisymposium features recent trends, from foundations and applications in time series analysis to models in physics and biology.

Organizer: Michael RosenblumUniversity of Potsdam, Germany

Organizer: Marc TimmeMax-Planck-Institute for Dynamics and Self-Organization, Germany

8:30-8:55 Data-Driven Network Inference: Achievements, Problems, Possible Research DirectionsKlaus Lehnertz, University of Bonn,

Germany

9:00-9:25 Data Based Modelling: Inferring the Direct Directed Network Structure from DataBjörn Schelter, University of Aberdeen,

United Kingdom; Marco Thiel, King’s College, University of Aberdeen, United Kingdom

9:30-9:55 Topology Predicts Dynamics; Dynamics Constrain TopologySrinivas Gorur-Shandilya, Yale

University, USA

10:00-10:25 Network Structure from Responses of Time-invariantsMor Nitzan, Hebrew University of

Jerusalem, Israel; Jose Casadiego and Marc Timme, Max-Planck-Institute for Dynamics and Self-Organization, Germany

Thursday, May 21

MS114Mathematical Modeling of Basal Ganglia8:30 AM-10:30 AMRoom:Magpie B

Basal ganglia is a set of subcortical brain structures involved in many different functions, including reinforcement learning and control of cognitive and motor programs. The impairment of the basal ganglia may lead to different disorders including Parkinson’s disease. The objective of this minisymposium is to present together moderns developments in the basal ganglia modeling in application to different aspects of basal ganglia function and dysfunction, such as dynamic patterns of activity in the basal ganglia, deep brain stimulation of the basal ganglia, and interaction of basal ganglia with brain’s cortex.

Organizer: Yixin GuoDrexel University, USA

Organizer: Leonid RubchinskyIndiana University - Purdue University Indianapolis, USA

8:30-8:55 Cortical Impact on the Dynamics of Subthalamo-pallidal NetworksLeonid Rubchinsky and Sungwoo Ahn,

Indiana University - Purdue University Indianapolis, USA; Elizabeth Zauber, Indiana University, USA; Robert Worth, Indiana University, USA

9:00-9:25 Oscillations and Action Selection in a Multi-Channel Model of the Basal GangliaRoman M. Borisyuk and Robert Merrison-

Hort, Plymouth University, United Kingdom

9:30-9:55 Possible Mechanisms for Generation of Beta Oscillations in Parkinson’s DiseaseAlexander Pavlides, University of Oxford,

United Kingdom; John Hogan, Bristol Centre for Applied Nonlinear Mathematics and University of Bristol, United Kingdom; Rafal Bogacz, University of Oxford, United Kingdom

10:00-10:25 Identifying and Tracking Transitions in Neural Spiking Dynamics in the Subthalamic Nucleus of Parkinson’s PatientsUri Eden, Boston University, USA


Thursday, May 21

MS121Engineering Applications of Non-smooth Dynamics - Part I of II8:30 AM-10:30 AMRoom:Primrose A

For Part 2 see MS133 Friction and impact are challenging research areas of engineering. These phenomena are commonly described by empirical models, such as the coefficient of restitution or various friction models, including the Coulomb-Amontons’ law. Modelling contact mechanics from first principles is almost impossible, each model needs some parameter fitting. Even when a model is available, one might not be able to solve it due to various mathematical singularities, where there is no unique prediction. This minisymposium shows a number of applications where the ‘rough’ terrain of non-smooth dynamics must be carefully navigated. Attempts will be also made to resolve singularities and identify contact force models.

Organizer: Robert SzalaiUniversity of Bristol, United Kingdom

8:30-8:55 Exploring Experimental Paths for Reliable Mathematical Models of FrictionThibaut Putelat, University of Bristol,

United Kingdom

9:00-9:25 Painlevé Paradox: Lessons That We Do Not Learn from Simple ExamplesPeter L. Varkonyi, Budapest University of

Technology and Economics, Hungary

9:30-9:55 Testing of a Spacecraft Structure with Non-Smooth NonlinearitiesLudovic Renson, J.P. Noel, and G.

Kerschen, University of Liege, Belgium

10:00-10:25 Nonlinear Dynamics and Bifurcations of Rotor-Stator Contact in Rotating MachinesNicholas Vlajic, National Institute of

Standards and Technology, USA; Alan R. Champneys, University of Bristol, United Kingdom; Michael Friswell and Kiran Vijayan, Swansea University of South Wales, United Kingdom

Thursday, May 21

MS120Stochastic Dynamics and Their Applications - Part I of II8:30 AM-10:30 AMRoom:White Pine

For Part 2 see MS132 Stochastic dynamical concepts are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. There are some theory results of the stochastic dynamics such as the stochastic attractors, invariant manifolds, invariant measures. However, the theory is restricted on some conditions. Applied science and engineering requires more stochastic dynamical techniques. The objective of this minisymposium is to bring the bridge between the new theory methods and approaches to stochastic dynamics in applications.

Organizer: Xiaopeng ChenPeking University, China

Organizer: Jinqiao DuanIllinois Institute of Technology, USA

8:30-8:55 Slow Manifolds and Interface Motion for Stochastic PDEsDirk Blömker, Universität Augsburg,

Germany

9:00-9:25 Slow Manifolds for a Nonlocal SpdeLu Bai, Huazhong University of Science &

Technology, China

9:30-9:55 Self-similarity in Stochastic PDEsWei Wang, Nanjing University, China

10:00-10:25 On the Complete Dynamical Behavior for Three Dimensional Stochastic Competitive Lotka-VolterraSystemsJifa Jiang, Shanghai Normal University,

China

Thursday, May 21

MS118Recent Advances on Multiple Timescale Dynamics - Part I of II8:30 AM-10:30 AMRoom:Superior A

For Part 2 see MS130 Multiple timescales are ubiquitous in models of real-world phenomena such as neuron firing, laser dynamics, and climatic rhythms. Differential equations involving variables evolving on distinct timescales yield rich and notoriously hard mathematical questions. This two-part minisymposium presents recent results on singularly perturbed ODEs, which is the most amenable paradigm for analysis of multiple timescale phenomena. We will give a panorama of this topic, from theoretical work on planar canard problems, in both smooth and non-smooth vector fields (Part I), to more application-driven studies of complex oscillations with at least three variables and two or more timescales (Part II).

Organizer: Mathieu DesrochesINRIA Paris-Rocquencourt, France

Organizer: Vivien KirkUniversity of Auckland, New Zealand

Organizer: Jonathan E. RubinUniversity of Pittsburgh, USA

8:30-8:55 Theoretical Analysis of Homoclinic CanardsJean-Pierre Francoise, Universite Pierre et

Marie Curie (Paris 6), France

9:00-9:25 Singular Bogdanov-Takens Bifurcations in the PlanePeter De Maesschalck, Hasselt University,

Belgium

9:30-9:55 Canard Orbits in Planar Slow-Fast Piecewise-Linear SystemsSoledad Fernandez-Garcia, Mathieu

Desroches, and Martin Krupa, INRIA Paris-Rocquencourt, France; Antonio E. Teruel, University of the Balearic Islands, Spain

10:00-10:25 Folded Nodes, Canards and Mixed Mode Oscilations in 3D Piecewise-Linear SystemsAntonio E. Teruel, University of the Balearic

Islands, Spain; Mathieu Desroches, INRIA Paris-Rocquencourt, France; Enrique Ponce, Universidad de Sevilla, Spain; Rafel Prohens, University of the Balearic Islands, Spain; Antoni Guillamon, Polytechnic University of Catalonia, Spain; Emilio Freire, Universidad de Sevilla, Spain


Thursday, May 21

MS6Analysis, Modeling, and Forecasting in Biomedicine1:30 PM-3:30 PMRoom:Magpie A

We will discuss how to use biomedical data to reconstruct and forecast state in different contexts. Specific topics include: (i) model-based forecasting of glucose in type 2 diabetics using sparsely collected data, (ii) model-based forecasting of sleep-wake cycles, (iii) prediction of recovery of consciousness in patients with severe brain injury using clinically collected data, and (iv), time series analysis and modeling using electronic health record data to discover and forecast drug side effects. The talks will focus integrating a diverse set of tools such as data assimilation, spectral time series analysis and Granger causality with real biomedical data.

Organizer: David J. AlbersColumbia University, USA

1:30-1:55 Time Series Modeling and Analysis Using Electronic Health Record DataGeorge Hripcsak, Columbia University,

USA

2:00-2:25 Predicting Recovery of Consciousness in Patients with Brain InjuryHans-Peter Frey, Columbia University,

USA

2:30-2:55 Model-Based Glucose Forecasting for Type 2 DiabeticsDavid J. Albers, Columbia University,

USA

3:00-3:25 Assimilating Sleep - Putting the Model to the DataBruce J. Gluckman, Pennsylvania State

University, USA

Thursday, May 21Red Sock Award Announcements11:00 AM-11:15 AMRoom:Ballroom

IP6Brain Control - It’s Not Just for Mad Scientists11:15 AM-12:00 PMRoom:Ballroom

Chair: Anthony J. Roberts, University of Adelaide, Australia

The brain is an amazing organ - and dynamical system - which is responsible for a number of important functions including cognition, attention, emotion, perception, memory, and motor control. Some brain disorders are hypothesized to have a dynamical origin; in particular, it has been been hypothesized that some symptoms of Parkinson’s disease are due to pathologically synchronized neural activity in the motor control region of the brain. We have developed a procedure for determining an optimal electrical deep brain stimulus which desynchronizes the activity of a group of neurons by maximizing the Lyapunov exponent associated with their phase dynamics, work that could lead to an improved “brain control” method for treating Parkinson’s disease. The use of related control methods for treating other medical disorders, including cardiac arrhythmias, will also be discussed.

Jeff MoehlisUniversity of California, Santa Barbara, USA

Lunch Break12:00 PM-1:30 PMAttendees on their own

Thursday, May 21

MS122Nonlinear Waves in Coupled Systems - Part I of II8:30 AM-10:30 AMRoom:Primrose B

For Part 2 see MS134 Traveling waves are special solutions of partial differential equations posed on infinite domains that have spatially homogeneous equilibria. They appear in many applications and attract interest not only because they represent coherent structures, but also because information about traveling waves helps to understand complex dynamics of the physical system and therefore is of importance for the general understanding of the underlying phenomenon. In this special session, we bring together researchers who study various aspects of nonlinear waves in coupled systems of partial differential equations using analytical and numerical techniques, in particular addressing the existence, stability, and speed selection issues.

Organizer: Anna GhazaryanMiami University and University of Kansas, USA

Organizer: Vahagn ManukianMiami University, USA

8:30-8:55 Nonlinear Waves in a Lugiato-Lefever ModelMariana Haragus, Université de Franche-

Comté, France

9:00-9:25 The Entry-exit Function and Geometric Singular Perturbation TheoryPeter De Maesschalck, Hasselt University,

Belgium; Stephen Schecter, North Carolina State University, USA

9:30-9:55 Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion EquationsKelly Mcquighan, Boston University, USA;

Bjorn Sandstede, Brown University, USA

10:00-10:25 Stability of Traveling Waves in a Model for a Thin Liquid Film FlowVahagn Manukian, Miami University, USA



Thursday, May 21

MS125CANCELLED - Data Driven Methods for Dynamical Systems1:30 PM-3:30 PMRoom:Ballroom III

In many applications driven by large-scale high-dimensional datasets, there is evidence of a coarse low-dimensional structure nonlinearly embedded in the ambient space. Modern nonlinear methods leverage these coarse geometric structures by constructing discrete approximations to operators, such at the Laplacian, which encode geometric information. Applying these methods to data generated by a dynamical system requires that they respect the time ordering, which is the fundamental structure of dynamics. In this special session we discuss recent developments and explore future ideas for finding coarse geometric structure in large-scale dynamical datasets with a time-ordering, including applications to improve prediction, and uncertainty quantification.

Organizer: Dimitrios GiannakisCourant Institute of Mathematical Sciences, New York University, USA

Organizer: Tyrus BerryPennsylvania State University, USA

Thursday, May 21

MS124Recent Insights into Controling Flow Structures - Part II of II1:30 PM-3:30 PMRoom:Ballroom II

For Part 1 see MS111 Interior flow entities such as fluid interfaces, coherent structures and invariant manifolds have a profound influence on transport in unsteady flows. The ability to control them is attracting much recent interest, fueled in part by emerging biotechnological applications at the microfluidic level. This minisymposium will cover a range of state-of-the-art approaches to controling flow structures which are inspired by dynamical systems methods.

Organizer: Sanjeeva BalasuriyaUniversity of Adelaide, Australia

Organizer: Marko BudisicUniversity of Wisconsin, Madison, USA

Organizer: Jean-Luc ThiffeaultUniversity of Wisconsin, Madison, USA

1:30-1:55 Multi-Objective Optimal Control of Transport and Mixing in FluidsKathrin Padberg-Gehle, Dresden

University of Technology, Germany; Sina Ober-Blöbaum, University of Paderborn, Germany

2:00-2:25 Input-Ouptut Analysis in Channel Flows and Implications for Flow ControlBassam A. Bamieh, University of

California, Santa Barbara, USA

2:30-2:55 Correlating Dynamical Structures with Forcing in 2D FlowNicholas T. Ouellette, Yale University,

USA

3:00-3:25 Nematic Liquid Crystal Flow in a Microfluid: Topological TransitionsLinda Cummings, New Jersey Institute

of Technology, USA; Thomas Anderson, California Institute of Technology, USA; Lou Kondic, New Jersey Institute of Technology, USA

Thursday, May 21

MS123Spatio-temporal Patterns in Ecology1:30 PM-3:30 PMRoom:Ballroom I

Many populations and ecosystems exhibit spatial structures, most often generated by interactions between the organisms themselves and their environment. This spatial self-organisation may appear as patterns in vegetation, in the form of flocks of birds or schools of fish. The underlying driving mechanisms and dynamics are for a large part not well-understood. Moreover, ecological questions about spatio-temporal dynamics often generate fundamental challenges to the mathematical theory. In this mini-symposium, various approaches are taken to study ecological and mathematical aspects of the formation of patterns in ecological systems.

Organizer: Vivi RottschaferLeiden University, Netherlands

Organizer: Arjen DoelmanLeiden University, Netherlands

1:30-1:55 Models of Patchy Invasion: A Mathematical Toy Or a New Paradigm?Sergei Petrovskii, University of Leicester,

United Kingdom

2:00-2:25 The Effect of Slow Spatial Processes in a Phytoplankton-Nutrient ModelLotte Sewalt and Arjen Doelman, Leiden

University, Netherlands; Antonios Zagaris, University of Twente, Netherlands

2:30-2:55 Stripe Pattern Selection by Advective RD Systems: Resilience of Banded Vegetation on SlopesEric Siero and Arjen Doelman, Leiden

University, Netherlands; Jens Rademacher, University of Bremen, Germany

3:00-3:25 Pattern-formation in Semiarid Vegetation: Using Bifurcation Theory for Model ComparisonSarah Iams, Northwestern University, USA

CANCELLE

D


Thursday, May 21

MS128Advances in Computer Assisted Proof for Infinite Dimensional Dynamical Systems1:30 PM-3:30 PMRoom:Wasatch B

When analyzing global dynamics of infinite dimensional dynamical systems numerical simulation and analytical methods are indispensable tools. Starting with the seminal work of Lanford and Eckmann, rigorous numerics aims at bridging the apparent gap between what can be computed and what can proved rigorously. Mathematically rigorous information on global dynamical features is obtained by starting from finite dimensional approximations of a dynamical scaffold (fixed points, traveling waves, periodic and connecting orbits). This minisymposium explores recent advances in rigorous numerics for topics such as pattern detection in higher order equations, global dynamics of parabolic PDEs and infinite dimensional maps.

Organizer: Christian P. ReinhardtVU University, Amsterdam, Netherlands

Organizer: Jason Mireles-JamesFlorida Atlantic University, USA

1:30-1:55 The Parametrization Method in Infinite DimensionsChristian P. Reinhardt, VU University,

Amsterdam, Netherlands; Jason Mireles-James, Florida Atlantic University, USA

2:00-2:25 Rigorous Numerics for Some Pattern Formation ProblemsJan Bouwe Van Den Berg, VU University,


2:30-2:55 Rigorous Numerics for Symbolic Dynamics and Topological Entropy BoundsSarah Day, College of William & Mary,

USA; Rafael Frongillo, University of California, Berkeley, USA

3:00-3:25 Orbital Stability Investigations for Travelling Waves in a Nonlinearly Supported BeamMichael Plum, Karlsruhe University,

Germany

Thursday, May 21

MS127Inverse Problems in Network Dynamics - Part II of II1:30 PM-3:30 PMRoom:Wasatch A

For Part 1 see MS115 Network Dynamics constitutes a rapidly expanding field with applications in natural and social science, medicine, engineering, and beyond. Commonly, mathematical scientists study how a specific network model behaves collectively as a function of parameters or inputs. Here, taking a complementary view, we ask what recorded time series from a network’s units and respective correlation and information measures tell us about the units’ local dynamics and their real physical interactions. Such inverse network dynamics are much less explored and even less understood. The minisymposium features recent trends, from foundations and applications in time series analysis to models in physics and biology.

Organizer: Michael RosenblumUniversity of Potsdam, Germany

Organizer: Marc TimmeMax-Planck-Institute for Dynamics and Self-Organization, Germany

1:30-1:55 Reconstructing Network Connectivity by Triplet AnalysisMichael Rosenblum, University of

Potsdam, Germany

2:00-2:25 Dynamic Information Routing in Complex NetworksChristoph Kirst, Rockefeller University,

USA

2:30-2:55 Unraveling Network Topology from Derivative-Variable CorrelationsZoran Levnajic, Laboratory of Data

Technologies, Slovenia

3:00-3:25 From Neural Dynamics to Network Properties and Cognitive FunctionDaniel Maruyama, Nicollette Ognjanovski,

Sara Aton, and Michal Zochowski, University of Michigan, USA

Thursday, May 21

MS126Voltage and Calcium Dynamics in Single Cells and Multicellular Systems1:30 PM-3:30 PMRoom:Magpie B

Cardiac cell contraction originates with a change in membrane potential that leads to a large release of calcium from intracellular stores and produce contraction. During normal function calcium follows voltage and contraction is uniform. However in disease or extremely fast pacing calcium and voltage coupling can change as well as their respective magnitudes, they can lead to period doubling bifurcations that in turn can produce complex spatiotemporal patterns and initiate arrhythmias. In this minisymposium we will present experimental results and theoretical mechanisms that describe some of the dynamics between calcium and voltage that can lead to cardiac arrhythmias.

Organizer: Flavio FentonGeorgia Institute of Technology, USA

Organizer: Yanyan YiGeorgia Institute of Technology, USA

1:30-1:55 Synchronization of Calcium Sparks and WavesDaisuke Sato, University of California,

Davis, USA

2:00-2:25 Nucleation and Dynamics of Spontaneous Ca Waves in Cardiac CellsYohannes Shiferaw, California State

University, Northridge, USA

2:30-2:55 Effects of Implementing Contraction to Calcium-Voltage ModelsYanyan Ji, Georgia Insitute of Technology,

USA and Jagiellonian University, Poland; Flavio M. Fenton, Georgia Institute of Technology, USA; Richard Gray, U.S. Food and Drug Administration, USA

3:00-3:25 Complex Dynamic Patterns of Voltage and Calcium in Mammalian HeartsIlija Uzelac and Flavio M. Fenton, Georgia

Institute of Technology, USA


2:30-2:55 Mixed-Mode Bursting Oscillations (MMBOs): Slow Passage Through a Spike-adding Canard ExplosionMathieu Desroches, INRIA Paris-

Rocquencourt, France; Tasso J. Kaper, Boston University, USA; Martin Krupa, INRIA Paris-Rocquencourt, France

3:00-3:25 Averaging, Folded Singularities and Torus Canards in a Coupled Neuron ModelKerry-Lyn Roberts, University of Sydney,

Australia; Jonathan E. Rubin, University of Pittsburgh, USA; Martin Wechselberger, University of Sydney, Australia

Thursday, May 21

MS130Recent Advances on Multiple Timescale Dynamics - Part II of II1:30 PM-3:30 PMRoom:Superior A

For Part 1 see MS118 Multiple timescales are ubiquitous in models of real-world phenomena such as neuron firing, laser dynamics, and climatic rhythms. Differential equations involving variables evolving on distinct timescales yield rich and notoriously hard mathematical questions. This two-part minisymposium presents recent results on singularly perturbed ODEs, which is the most amenable paradigm for analysis of multiple timescale phenomena. We will give a panorama of this topic, from theoretical work on planar canard problems, in both smooth and non-smooth vector fields (Part I), to more application-driven studies of complex oscillations with at least three variables and two or more timescales (Part II).

Organizer: Mathieu DesrochesINRIA Paris-Rocquencourt, France

Organizer: Vivien KirkUniversity of Auckland, New Zealand

Organizer: Jonathan E. RubinUniversity of Pittsburgh, USA

1:30-1:55 Three Timescale Phenomena in Coupled Morris-Lecar EquationsPingyu Nan, University of Auckland, New

Zealand; Yangyang Wang, University of Pittsburgh, USA; Vivien Kirk, University of Auckland, New Zealand; Jonathan E. Rubin, University of Pittsburgh, USA

2:00-2:25 An Organizing Center for Spatiotemporal BurstingAlessio Franci, University of Cambridge,

United Kingdom; Guillaume Drion, Brandeis University, USA; Rodolphe Sepulchre, University of Cambridge, United Kingdom

Thursday, May 21

MS129Complex Collective Dynamics of Oscillator Networks - Part II of II1:30 PM-3:00 PMRoom:Maybird

For Part 1 see MS117 Considerable progress has recently been made in understanding the collective dynamics of large oscillator networks. New analytical tools have been created and extended in their applicability, and novel effects have been demonstrated not only theoretically and numerically, but also experimentally. Results in this field have broad application to both physical and biological systems. Part one of this symposium will report recent general mean field results involving chimera states, assortative networks, and generalizations of the classic Kuramoto model. Part two will focus on networks of neuronal oscillators, their relationship to field models, and the dynamical consequences of connectivity.

Organizer: Paul SoGeorge Mason University, USA

Organizer: Arkady PikovskyUniversity of Potsdam, Germany

Organizer: Ernest BarretoGeorge Mason University, USA

1:30-1:55 Neural Field Models Which Include Gap JunctionsCarlo R. Laing, Massey University, New

Zealand

2:00-2:25 From Ensembles of Pulse-Coupled Oscillators to Firing-Rate ModelsDiego Pazó, Instituto de Física de Cantabria

(IFCA), Spain; Ernest Montbrio, Universitat Pompeu Fabra, Spain; Alex Roxin, Centre de Recerca Matemàtica, Spain

2:30-2:55 Suppressing Complex Collective Behavior in a Network of Theta Neurons by Synaptic DiversityLucas Lin, Thomas Jefferson High School

of Science and Techonology, USA; Ernest Barreto and Paul So, George Mason University, USA



Thursday, May 21

MS133Engineering Applications of Non-smooth Dynamics - Part II of II1:30 PM-3:30 PMRoom:Primrose A

For Part 1 see MS121 Friction and impact are challenging research areas of engineering. These phenomena are commonly described by empirical models, such as the coefficient of restitution or various friction models, including the Coulomb-Amontons’ law. Modelling contact mechanics from first principles is almost impossible, each model needs some parameter fitting. Even when a model is available, one might not be able to solve it due to various mathematical singularities, where there is no unique prediction. This minisymposium shows a number of applications where the ‘rough’ terrain of non-smooth dynamics must be carefully navigated. Attempts will be also made to resolve singularities and identify contact force models.

Organizer: Robert SzalaiUniversity of Bristol, United Kingdom

1:30-1:55 Contact and Friction Within Geometrically Exact Shell Theory - Modeling Microslip and Dissipation in Structural SystemsD Dane Quinn, University of Akron, USA

2:00-2:25 A New Semi-Analytical Algorithm for Two-Dimensional Coulomb Frictional SystemXiaosun Wang, Wuhan University, China;

Jim Barber, University of Michigan, USA

2:30-2:55 Lessons Learnt from the Two-Ball Bounce ProblemYani Berdeni, University of Bristol, United

Kingdom

3:00-3:25 Predicting Conditions for Self-sustained Vibration in DrillstringsTore Butlin, University of Cambridge,

United Kingdom

Thursday, May 21

MS132Stochastic Dynamics and Their Applications - Part II of II1:30 PM-3:00 PMRoom:White Pine

For Part 1 see MS120 Stochastic dynamical concepts are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. There are some theory results of the stochastic dynamics such as the stochastic attractors, invariant manifolds, invariant measures. However, the theory is restricted on some conditions. Applied science and engineering requires more stochastic dynamical techniques. The objective of this minisymposium is to bring the bridge between the new theory methods and approaches to stochastic dynamics in applications.

Organizer: Xiaopeng ChenPeking University, China

Organizer: Jinqiao DuanIllinois Institute of Technology, USA

1:30-1:55 How to Quantify Non-Gaussian Stochastic Dynamics?Jinqiao Duan, Illinois Institute of

Technology, USA

2:00-2:25 Random Dynamical Systems for Non-Densely Defined Evolution EquationsAlexandra Neamtu, Friedrich Schiller

Universität Jena, Germany

2:30-2:55 Stochastic Center Manifolds Without Gap ConditionsXiaopeng Chen, Peking University, China

Thursday, May 21

MS131Uncertainty Propogation in High Dimensional Systems1:30 PM-3:30 PMRoom:Superior B

Uncertainty can be found everywhere in real control systems, from the sensor readings to the dynamics themselves. Given incomplete knowledge one must have a means of estimating the likelihood of a given event, such as the toppling over of a robotic walker. In terms of computation, this is a substantially greater challenge than deterministic prediction. Computing likelihood boils down to computing the advection of a probability density. This is typically an infinite dimensional inverse problem. In this series of talks we present a range of approaches for attacking this problem numerically.

Organizer: Henry O. JacobsImperial College London, United Kingdom

Organizer: Ram VasudevanUniversity of Michigan, USA

1:30-1:55 Optimal Control Design and Value Function Estimation for Nonlinear Dynamical SystemsMilan Korda, École Polytechnique Fédérale

de Lausanne, Switzerland

2:00-2:25 Transfer Operator Methods for Stability Analysis and ControlUmesh Vaidya, Iowa State University, USA

2:30-2:55 Unitary Representations of Diffeomorphisms: Halfway Between Koopmanism and Transfer Operator TheoryHenry O. Jacobs, Imperial College London,

United Kingdom

3:00-3:25 Numerical Advection of Probability Densities for High Dimensional SystemsRam Vasudevan, University of Michigan,

USA


Thursday, May 21Closing Remarks4:00 PM-4:15 PMRoom:Ballroom

IP7The Robotic Scientist: Distilling Natural Laws from Raw Data, from Robotics to Biology and Physics4:15 PM-5:00 PMRoom:Ballroom

Chair: Timothy Sauer, George Mason University, USA

Can machines discover scientific laws automatically? Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. This talk will outline a series of recent research projects, starting with self-reflecting robotic systems, and ending with machines that can formulate hypotheses, design experiments, and interpret the results, to discover new scientific laws. We will see examples from psychology to cosmology, from classical physics to modern physics, from big science to small science.

Hod LipsonCornell University, USA

Thursday, May 21

MS134Nonlinear Waves in Coupled Systems - Part II of II1:30 PM-3:30 PMRoom:Primrose B

For Part 1 see MS122 Traveling waves are special solutions of partial differential equations posed on infinite domains that have spatially homogeneous equilibria. They appear in many applications and attract interest not only because they represent coherent structures, but also because information about traveling waves helps to understand complex dynamics of the physical system and therefore is of importance for the general understanding of the underlying phenomenon. In this special session, we bring together researchers who study various aspects of nonlinear waves in coupled systems of partial differential equations using analytical and numerical techniques, in particular addressing the existence, stability, and speed selection issues.

Organizer: Anna GhazaryanMiami University and University of Kansas, USA

Organizer: Vahagn ManukianMiami University, USA

1:30-1:55 An Overview of Evans Function ComputationJeffrey Humpherys, Brigham Young

University, USA

2:00-2:25 Invasion Fronts in Systems of Reaction Diffusion EquationsMatt Holzer, George Mason University,

USA

2:30-2:55 Orbital Stability of Waves Traveling Along Vortex FilamentsStéphane Lafortune, College of

Charleston, USA

3:00-3:25 Stability of Combustion Fronts in Hydraulically Resistant Porous MediaAnna Ghazaryan, Miami University, USA



Save the Date!2017 SIAM Conference on

Applications of Dynamical Systems

May 21-25, 2017

Snowbird Ski and Summer Resort

Snowbird, Utah, USA

7

2017

21-25,


Save the Dates!


Notes


DS15 Abstracts

2015

Abstracts are printed as submitted by the authors.

88 DS15 Abstracts

IP1

Advances on the Control of Nonlinear Network Dy-namics

An increasing number of complex systems are now mod-eled as networks of coupled dynamical entities. Nonlinear-ity and high-dimensionality are hallmarks of the dynam-ics of such networks but have generally been regarded asobstacles to control. In this talk, I will discuss recent ad-vances on mathematical and computational approaches tocontrol high-dimensional nonlinear network dynamics un-der general constraints on the admissible interventions. Iwill present applications to the stabilization of power grids,identification of new therapeutic targets, mitigation of ex-tinctions in food webs, and control of systemic failures insocio-economic systems. These examples will illustrate thepotential and limitations of existing methods to address abroad class of problems, ranging from cascade control andtransient stability to network reprogramming in general.

Adilson E. MotterNorthwestern [email protected]

IP2

Mathematics of Crime

There is an extensive applied mathematics literature devel-oped for problems in the biological and physical sciences.Our understanding of social science problems from a math-ematical standpoint is less developed, but also presentssome very interesting problems, especially for young re-searchers. This lecture uses crime as a case study for usingapplied mathematical techniques in a social science appli-cation and covers a variety of mathematical methods thatare applicable to such problems. We will review recentwork on agent based models, methods in linear and non-linear partial differential equations, variational methodsfor inverse problems and statistical point process models.From an application standpoint we will look at problemsin residential burglaries and gang crimes. Examples willconsider both ”bottom up’ and ”top down’ approaches tounderstanding the mathematics of crime, and how the twoapproaches could converge to a unifying theory.

Andrea L. BertozziUCLA Department of [email protected]

IP3

Filtering Partially Observed Chaotic DeterministicDynamical Systems

This talk is concerned with determining the state of achaotic dynamical system, for which the initial conditionis only known probabilisticlly, given partial and noisy ob-servations. In particular it is of interest to study this prob-lem in the limit of a large number of such observations,over a long time interval. A key question is to deter-mine which observations are sufficient in order to accu-rately recover the signal, and thereby overcome the lackof predictability caused by sensitive dependence on ini-tial conditions. A canonical application is the develop-ment of probabilistic weather forecasts. In order to studythis problem concretely, we will focus on a wide class ofdissipative differential equations with quadratic energy-conserving nonlinearity, including the Navier-Stokes equa-tion on a two dimensional torus. The work presented iscontained in the paper D. Sanz-Alonso and A.M.Stuart,

”Long-time asymptotics of the filtering distribution forpartially observed chaotic deterministic dynamical sys-tems” (http://arxiv.org/abs/1411.6510); see also the pa-per K.J.H. Law, A. Shukla and A.M. Stuart, ”Analysisof the 3DVAR filter for the partially observed Lorenz ’63model,’” Discrete and Continuous Dynamical Systems A,34(2014), and the book K.J.H. Law, A.M.Stuart and K.Zygalalkis, ”Data Assimilation: A Mathematical Introduc-tion” (in preparation, 2015) for further background refer-ences.

Andrew StuartMathematics Institute,University of [email protected]

IP4

Fields of Dreams: Modeling and Analysis of LargeScale Activity in the Brain

With the advent of optogenetics and the ability to recordlarge numbers of neurons with high temporal resolution,there is now a great deal of interest in both the tempo-ral and spatial activity of neurons in the brain. In thistalk, I will discuss a number of old and new developmentsin the study of these nonlinear integro-differential equa-tions and how they apply to some new biological find-ings. Topics that I will discuss include the role of noise onspatio-temporal activity, the interaction between extrinsicand intrinsic activity, interactions between multiple spatialnetworks, and finally some recent applications of Filippovtheory to discontinuous neural field models.

Bard ErmentroutUniversity of PittsburghDepartment of [email protected]

IP5

Cooperation, Cheating, and Collapse in BiologicalPopulations

Natural populations can suffer catastrophic collapse in re-sponse to small changes in environmental conditions asa result of a bifurcation in the dynamics of the system.We have used laboratory microbial ecosystems to directlymeasure theoretically proposed early warning signals ofimpending population collapse based on critical slowingdown. Our experimental yeast populations cooperativelybreak down sugar, meaning that below a critical size thepopulation cannot sustain itself. The cooperative nature ofyeast growth on sucrose makes the population susceptibleto ”cheater” cells, which do not contribute to the publicgood and reduce the resilience of the population.

Jeff GoreMassachusetts Institute of [email protected]

IP6

Brain Control - It’s Not Just for Mad Scientists

The brain is an amazing organ - and dynamical system -which is responsible for a number of important functions in-cluding cognition, attention, emotion, perception, memory,and motor control. Some brain disorders are hypothesizedto have a dynamical origin; in particular, it has been beenhypothesized that some symptoms of Parkinson’s diseaseare due to pathologically synchronized neural activity in

DS15 Abstracts 89

the motor control region of the brain. We have developed aprocedure for determining an optimal electrical deep brainstimulus which desynchronizes the activity of a group ofneurons by maximizing the Lyapunov exponent associatedwith their phase dynamics, work that could lead to an im-proved ”brain control” method for treating Parkinson’s dis-ease. The use of related control methods for treating othermedical disorders, including cardiac arrhythmias, will alsobe discussed.

Jeff MoehlisDept. of Mechanical EngineeringUniversity of California – Santa [email protected]

IP7

The Robotic Scientist: Distilling Natural Lawsfrom Raw Data, from Robotics to Biology andPhysics

Can machines discover scientific laws automatically? De-spite the prevalence of computing power, the process offinding natural laws and their corresponding equations hasresisted automation. This talk will outline a series of re-cent research projects, starting with self-reflecting roboticsystems, and ending with machines that can formulate hy-potheses, design experiments, and interpret the results, todiscover new scientific laws. We will see examples frompsychology to cosmology, from classical physics to modernphysics, from big science to small science.

Hod LipsonCornell University, [email protected]

SP1

Juergen Moser Lecture - Dynamics and Data

This lecture highlights interdisciplinary interactions of dy-namical systems theory. Experimental data and computersimulation have inspired mathematical discoveries, whileresulting theory has made successful predictions and cre-ated new scientific perspectives. Nonlinear dynamics hasunified diverse fields of science and revealed deep mathe-matical phenomena. Examples involving

• One dimensional maps

• Numerical bifurcation analysis

• Multiple time scales

• Bursting and MMOs in neuroscience and chemistry

• Locomotion

are described, along with emerging areas having public im-pact.

John GuckenheimerCornell [email protected]

CP1

Morse-Floer Homology for Travelling Waves inReaction-Diffusion Equations

This talk is about heteroclinic solutions u of

∂2t u− c∂tu+Δxu+ f(u) = 0.

For suitable (nonlocal) perturbations of this equation solu-tions can be assigned an index, and solutions with a fixed

index form a finite dimensional manifold. Furthermore,for a large class of nonlinearities f we can count index 1solutions. This allows us to define Morse-Floer homologygroups, which are invariant with respect to continuation off .

Berry Bakker, Jan Bouwe Van Den Berg, Robert van DerVorstVU University [email protected], [email protected], [email protected]

CP1

Reaction-Diffusion Equations with Spatially Dis-tributed Hysteresis in Higher Spatial Dimensions

Many chemical and biological processes are modelled byreaction-diffusion equations with a nonlinearity involvinghysteresis. In such problems each spatial point can be inone of two configurations and the configuration changes intime via a hysteresis law. Points in different configurationssegregate the domain into several subdomains and switch-ing implies that these subdomains are separated by freeboundaries. We will discuss how the hysteresis gives riseto a novel type of free boundary evolution.

Mark J. CurranFree University of [email protected]

CP1

Existence of Periodic Solutions of the FitzHugh-Nagumo Equations for An Explicit Range of theSmall Parameter

We consider the FitzHugh-Nagumo system describingnerve impulse propagation in an axon. With aid ofcomputer-assisted rigorous computations we are able toshow the existence of the periodic pulse for an explicitrange of singular perturbation parameter ε ∈ (0, ε0]. Ourright bound ε0 is large enough to be reached by validatedcontinuation methods designed for ODEs without timescale separation.

Aleksander Czechowski, Piotr ZgliczynskiJagiellonian University, [email protected], [email protected]

CP1

Spatio-Temporal Dynamics of Heterogeneous Ex-citable Media

The propagation of electrical waves in biological tissue orconcentration waves in chemical reactions are examplesfor complex dynamics in excitable media. Already sim-ple homogeneous reaction-diffusion systems reveal a richdiversity of dynamical patterns, including spiral wavesand spatio-temporal chaos. Here we consider excitablemedia including heterogeneities and study their (tran-sient) dynamics in numerical simulations employing (co-variant) Lypaunov Vectors, (linear) mode decompositions,and diffusion-mapped delay coordinates.

Thomas LilienkampMax Planck Institute for Dynamics and Self-OrganizationBiomedical Physics Research [email protected]

Ulrich Parlitz, Stefan Luther

90 DS15 Abstracts

Max Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected], [email protected]

CP1

Low Dimensional Models of Diffusion and Reactionin Stratified Micro Flows

We develop a low dimensional model of simultaneous in-terphase mass transfer and reaction in two-phase stratifiedflows through microchannels. Here, diffusion quickly equi-librates the distribution of species in the lateral direction.This singularly perturbed dynamical system has a slowinvariant manifold, which is parameterized by a suitablyweighted laterally averaged concentration. The Lyapunov-Schmidt reduction of bifurcation theory is used to computethis manifold and derive reduced order models for arbitraryreaction kinetics.

Jason R. Picardo, Subramaniam PushpavanamDepartment of Chemical EngineeringIndian Institute of Technology [email protected], [email protected]

CP1

Defect Solutions in Reaction-Diffusion Equations

In this talk, I will discuss the effect a heterogeneity canhave on the pattern formation process for two differenttypes of reaction-diffusion equations. These heterogeneitiesfor example arise in models where a particular species isonly produced in a particular part of the domain of interest.I will mainly focus on the pinning of solutions near andaway from the heterogeneity.

Peter van HeijsterMathematical Sciences SchoolQueensland University of [email protected]

CP2

Generalized Behavior of the Two-phase System in(1+1) D

The two-phase model is well known for its applications ingel-dynamics. A network made of an extracellular poly-meric substance (EPS) is immersed in a fluid solvent. Thenetwork provides a layer of protection for bacterial growth.We find a general reduction in the two-phase system for anarbitrary growth in (1+1) D to a system of a single vari-able. This system emits several solutions. The first twosolutions show that in the presence of logistic growth ina frictionless environment, osmotic pressure has a negli-gible effect. The third solutions shows that the inviscidtwo-phase system emits shocks and rarefactions.

David A. Ekrut, Nicholas CoganFlorida State [email protected], [email protected]

CP2

Scaling and Robustness of Two Component Mor-phogen Patterning Systems

Embryonic development requires highly reproduciblemechanisms of pattern formation so that cell fate is as-signed at the right time and location. To identify themechanisms of pattern regulation, we developed a Two

Component System (TCS) model of morphogen (m) andmodulator (M) that interact and spatially alter the bio-chemical properties of each other. We identified a num-ber of network motifs that confer scaling and robustness ofmorphogen patterning including bilateral repression andothers.

Md. Shahriar KarimPurdue [email protected]

Hans G. OthmerUniversity of MinnesotaDepartment of [email protected]

David UmulisDept. of Ag. and Biological Engineering, PurdueUniversityWest Lafayette, IN-47904, [email protected]

CP2

Solitary Waves in the Excitable Discrete Burridge-Knopoff Model

The Burridge-Knopoff model describes the dynamics of anelastic chain of blocks pulled over a surface. This modelaccounts for nonlinear friction phenomena and displays ex-citability when the velocity-dependent friction force is non-monotone. We introduce a simplified piecewise linear fric-tion law (reminiscent of the McKean nonlinearity in spikingneuron models) which allows us to analyze the existenceof large amplitude solitary waves. Propagation failure isshown to occur for weakly coupled oscillators.

Jose Eduardo Morales MoralesINRIA Rhone [email protected]

Guillaume James, Arnaud TonnelierINRIA - Rhone [email protected], [email protected]

CP2

Aspects and Applications of Generalized Synchro-nization

Different concepts of generalized synchronization of cou-pled (chaotic) dynamical systems and corresponding timeseries analysis methods are revisited and compared. Fur-thermore, we address the relation to snapshot attractorsas well as potential applications of generalized synchro-nization for state estimation and data assimilation. For alltopics representative examples will be given to illustratethe main statements.

Ulrich ParlitzMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected]

CP2

Discrete Synchronization of Massively ConnectedSystems Using Hierarchical Couplings

We study the synchronization of massively connected net-works of which interactions come from successive hierar-

DS15 Abstracts 91

chical couplings. Motivations of this work come from thegrowing necessity of understanding properties of complexsystems that often exhibit a hierarchical structure. Start-ing with a set of 2n coupled maps, we obtain synchroniza-tion results for infinitely many, i.e for a Cantor set of maps.We also prove synchronization happens when the networkis still massively connected but with an infinite number ofbroken links inside the hierarchical structure.

Camille [email protected]

CP2

Nonlinear Dynamics of Two-Colored Filaments

Propagation of light filaments is a highly nonlinear processthat results from light-matter interactions. It is impor-tant area in nonlinear optics with much ongoing theoreti-cal and experimental research efforts. While there has beenmuch progress in both fronts, there remain many challengesto produce long-lived filaments. Modeling requires goodunderstanding of light matter interactions with a particu-lar objective of determining conditions that limits spatio-temporal instabilities thus producing quasi-stable dynam-ics. While typical studies concentrate on optical filamentsat a single frequency, mostly in the infrared (IR) and the ul-traviolet (UV) wavelengths, under suitable conditions non-linear wave-mixing can lead to multicolored filaments. Inthis talk I will present new results that consider the co-existence of UV/IR filaments under a variety of spatialconfigurations

Alexey Sukhinin, Alejandro AcevesSouthern Methodist [email protected], [email protected]

CP3

Heterogeneities in Temporal Networks Emergingfrom Adaptive Social Interactions

Recent studies on social empirical data have revealed het-erogeneities in human dynamics, which are signs of thedistinctive mechanism underlying the dynamical behaviorsof societies. It is known that human activity is bursty,and the social interactions have scale-free structures. Tofacilitate unified understanding of social dynamics and net-works, we propose a model of adaptive temporal networks.Under suitable conditions, this model exhibits heteroge-neous temporal and structural behaviors even from a com-pletely homogenous initial condition.

Takaaki AokiFaculty of EducationKagawa [email protected]

Luis RochaDepartment of Public Health SciencesKarolinska Institutet, Solna, [email protected]

Thilo GrossDepartment of Engineering Mathematics and BristolCentre forUniversity of Bristol, Bristol, UK

[email protected]

CP3

Analysis of Connected Vehicle Networks with Non-trivial Connectivity, a Modal Decomposition Ap-proach

Connected vehicles that communicate via wireless vehicle-to-vehicle communication are gaining increasing attentiondue to their potential in improving traffic safety, mobil-ity, and efficiency. As connected vehicle systems becomemore complex, the analysis of the arising networked dy-namical systems becomes more challenging. We present anovel method to analyze the network modes by expansionaround a network of simple connectivity, and demonstratethat unstable traffic flow can be stabilized using long-rangeinteractions.

Sergei S. AvedisovUniversity of Michigan, Ann [email protected]

Gabor OroszUniversity of Michigan, Ann ArborDepartment of Mechanical [email protected]

CP3

Simulating the Dynamics of College Drinking

Heavy episodic or binge drinking is among the most diffi-cult public health challenges on college campuses. Integrat-ing peer influence models from public health and identityverification from social psychology as mechanisms that in-fluence drinking behavior, we develop an agent-based simu-lation to examine the dynamics of drinking events, as stu-dents group together and interact. We also consider theconditions necessary for widely-used social norms interven-tions to be effective.

Ben G. Fitzpatrick, Jason Martinez, Elizabeth PolidanTempest [email protected], [email protected], [email protected]

CP3

Integrating Hydrological and Waterborne DiseaseNetwork Models

Mechanistic drivers of the seasonal patterns of cholera inBangladesh remain poorly understood. A community net-work model for cholera dynamics is developed. A hydro-logical model for the Ganges-Brahmaputra-Meghna riverbasin is integrated into the disease network model to ac-count for seasonality of surface water connectivity and con-tamination. We demonstrate that the integrated model cancontribute to the understanding of disease dynamics andpotentially to the development of disease forecasting tools.

Karly JacobsenMathematical Biosciences InstituteThe Ohio State [email protected]

Michael KellyThe Ohio State [email protected]

92 DS15 Abstracts

Faisal HossainUniversity of [email protected]

Joseph H. TienOhio State UniversityDepartment of [email protected]

CP3

Phase Response Properties of Collective Rhythmsin Networks of Coupled Dynamical Systems

Phase response property of a network of diffusively cou-pled dynamical units undergoing collective oscillations isstudied. Each unit can possess arbitrary local dynamicsas long as the whole coupled system exhibits stable limit-cycle oscillations. The phase response property of the sys-tem can be decomposed into Laplacian eigenmodes of thecoupling network, which reveals how each individual modecontributes to the total phase response. Phase synchro-nization of simple dynamical networks is analyzed as anexample.

Hiroya NakaoGraduate School of Information Science and Engineering,Tokyo Institute of [email protected]

Sho YasuiGraduate School of Information Science and EngineeringTokyo Institute of [email protected]

CP4

Prediction in Projection

Full and accurate reconstruction of dynamics from time-series data—e.g., via delay-coordinate embedding—is areal challenge in practice. For the purposes of forecast-ing, however, reconstructions that do not satisfy the di-mension conditions of the embedding theorems can stillbe quite useful. Despite the lack of topological conjugacy,near-neighbor forecast methods working in these reduced-order spaces are as (or more) effective than in completeembeddings. We demonstrate this using both syntheticand experimental time series data.

Joshua GarlandUniversity of Colorado at [email protected]

Elizabeth BradleyUniversity of ColoradoDepartment of Computer [email protected]

CP4

Sparse Sensing Based Detection of Dynamical Phe-nomena and Flow Transitions

Reduced order models for fluid dynamics are often sensitiveto changes in flow topology and require some informationabout the dynamical regime of operation. Using sparsesensing and reconstruction techniques, we present a frame-work to detect dynamical phenomena such as bifurcationsand changes in flow topology in a variety of thermo-fluiddynamical systems. This framework can be combined with

adaptive reduced order models for improved observationand control. We present some numerical results for thecase of Navier Stokes and Boussinesq equations.

Piyush GroverMitsubishi Electric Research [email protected]

Boris KramerVirginia [email protected]

Petros Boufounos, Mouhacine BenosmanMitsubishi Electric Research [email protected], [email protected]

CP4

Bifold Visualization of Dynamic Networks

We consider binary datasets arising from bipartite data,where the data describes the relationships between twotypes of entities (such as a user “liking’ a certain movie).Comparing the binary patterns between entities providesa dissimilarity measure which allows projecting that datain a Euclidean representation. We apply our algorithmto datasets of US senators and their voting records. Bysimultaneously representing intergroup and intragroup re-lationships, significant additional insight is provided by thevisualization.

Yazhen Jiang, Joseph Skufca, Jie SunClarkson [email protected], [email protected],[email protected]

CP4

An Algorithmic Approach to Computing LatticeStructures of Attractors

We describe the lifting of sublattices of attractors, whichare computationally less accessible, to lattices of forwardinvariant sets and attracting neighborhoods, which arecomputationally accessible. We provide necessary and suf-ficient conditions for such a lift to exist along with algo-rithms to check whether such conditions are met or not andto construct the lift if met. We illustrate the algorithmswith some examples.

Dinesh KastiFlorida Atlantic [email protected]

William D. KaliesFlorida Atlantic UniversityDepartment of Mathematical [email protected]

Robertus VandervorstVrije Universiteit [email protected]

CP4

Expanded Mixed Finite Element Method for Gen-eralized Forchheimer Flows

We study the expanded mixed finite element method ap-plied to the Forchheimer fluid flow in porous media. Thebounds for the solutions are established. Utilizing the spe-

DS15 Abstracts 93

cial properties of Forchheimer equation and boundedness ofsolutions we prove the optimal error estimates in L2-normfor solution. The error bounds are established for the so-lution and divergence of the vector variable in Lebesguenorms and Sobolev norms. A numerical example usingthe lowest order Raviart-Thomas (RT0) mixed element areprovided agreement with our theoretical analysis.

Thinh T. KieuUniversity of North [email protected]

Akif IbraguimovDepartment of Mathematics and Statistics.Texas Tech [email protected]

CP4

A Method for Identification of Spatially-VaryingParameters Despite Missing Data with Applica-tion to Remote SensingA Method for Identificationof Spatially-Varying Parameters Despite MissingData with Application to Remote Sensing

Remote sensing data allows for ecological inferences overlarge-scale oceanic regions. Proposed models require pa-rameter tuning to match data observations, including syn-chronization and filtering methods. A major hindrance inapplying synchronization methods to remote sensing datais the frequency with which clouds hide parts of a satelliteimage. A synchronization method is discussed to infer un-known model parameters and states, despite hidden data.We treat a PDE as a temporally-varying network to provethe method.

Sean Kramer, Erik BolltClarkson [email protected], [email protected]

CP5

A Mathematical Model for the Sexual Selection ofExtravagant and Costly Mating Displays

The evolution of extravagant and costly ornaments on an-imals has intrigued biologists and mathematicians sinceDarwin suggested that female preference for exaggeratedcourtship displays drives the sexual selection of these or-naments. We propose a minimal mathematical model thatincorporates two components of ornament evolution: anintrinsic cost and/or benefit of ornamentation to an indi-vidual, and a social benefit of relatively large ornamentswithin a population. Using bifurcation analysis and per-turbation theory, we show that on an evolutionary timescale, identically healthy animals will split into two niches,one with large ornaments and one with small. This resultmay explain why ecologists have observed bimodal distri-butions of ornament size in several species.

Sara CliftonNorthwestern University, [email protected]

Daniel Abrams, Daniel ThomasNorthwestern [email protected],

[email protected]

CP5

Mathematical Models of Seasonally Migrating Pop-ulations

Predator-prey systems that allow for one or more speciesto undergo mass migration open up a range of new possi-bilities from a dynamical point of view. We consider twodifferent approaches to modelling problems of this type,namely, ordinary and partial differential equations. In bothcases the inclusion of time switches is key to understand-ing their behaviour and allows us to consider the effectsof timing mismatches brought about by changing climaticconditions.

John G. DonohueNational University of Ireland, [email protected]

Petri T. PiiroinenSchool of Mathematics, Statistics and AppliedMathematicsNational University of Ireland, [email protected]

CP5

A Model for Mountain Pine Beetle Outbreaks inAn Age Structured Forest: Approximating Sever-ity and Outbreak-Recovery Cycle Period

We develop a system of difference equations to model(temperature-driven) mountain pine beetle infestation inan age-structured forest. Equilibrium stability analysisindicates the existence of periodic outbreaks that inten-sify as growth rates increase. Analytical methods are de-vised to predict outbreak severity, duration, and frequency.The model predicts cycle periods that fall within observedoutbreak period ranges. To assess future beetle impacton forests, we predict severity of outbreaks in the face ofchanging climate.

Jacob P. Duncan, James Powell, Luis GordilloUtah State [email protected], [email protected],[email protected]

Joseph EasonUniversity of [email protected]

CP5

Host-Mediated Responses on the Dynamics ofHost-Parasite Interaction

The regulation of helminth populations within hosts de-pends on host age, immunity and density-dependent con-straints. Laboratory infections reveal that rabbit immu-nity limits worm growth and reduces fecundity. Continu-ous natural exposure of rabbits to worms generates a neg-ative relationship between rabbit age and worm fecundity.Using an age-structured population model we show howthese regulatory factors stabilize the dynamical behaviourof between-host transmission via egg shedding throughmaintaining a self-sustained oscillation in rabbit genera-tions.

Suma Ghosh, Matthew Ferrari

94 DS15 Abstracts

The Pennsylvania State [email protected], [email protected]

CP5

Geometric Dissection of a Model for the Dynamicsof Bipolar Disorders

We study a model for the dynamics of bipolar disordersdeveloped by A. Goldbeter. The model is four-dimensionaland not in the standard form of slow-fast systems. Thegeometric analysis of the model is based on identifying andusing hierarchies of local approximations based on various- hidden – forms of time scale separation. A central toolin the analysis is the blow-up method which allows theidentification of a complicated singular cycle.

Ilona KosiukMPI MiSInselstrasse 22, 04103 Leipzig [email protected]

Ekaterina KutafinaAGH University of Science and TechnologyCracow, [email protected]

Peter SzmolyanVienna University of TechnologyVienna, [email protected]

CP6

Continuation of Bifurcations in Physical Experi-ments

A good mathematical model for a specific physical sys-tem can be hard to create. Fortunately, the low cost andeasy availability of high-speed electronics now enables real-time integration of numerical methods and physical ex-periments. This opens up a wide range of new possibil-ities in experimental nonlinear dynamics. Here we outlinethe current state-of-the-art in control-based continuation, amethod for tracking the solutions and bifurcations directlyin a physical experiment.

David A. BartonUniversity of Bristol, [email protected]

CP6

Structuring and Stability of Solutions of the StaticCahn-Hilliard Equation

We use the variational form of the 2D Cahn-Hilliard equa-tion to obtain numerically the steady non-linear solutionsof films of confined polymer blends with a free deformablesurface. Varying the average composition and geometryof the films we find a rich morphology of solutions in theform of laterally structured films, layered, droplets over thesubstrate and free surface, and checkerboard structures.We show that laterally structured films are energeticallyfavorable and that most of the solutions appear throughpitchfork bifurcations.

Santiago MadrugaAerospace Engineering SchoolUniversidad Politecnica de [email protected]

Fathi BribeshDepartment of MathematicsZawia University, Zawia, [email protected]

Uwe ThieleInstitute of Theoretical PhysicsUniversity of [email protected]

CP6

Escape from Potential Wells in Multi-Degree ofFreedom Systems: Phase Space Geometry and Par-tial Control

Predicting the escape from a potential energy well is a uni-versal exercise, governing myriad engineering and naturalsystems, e.g., buckling phenomena, ship capsize, and hu-man balance. For such systems, tube dynamics providesthe phase space criteria for escape. We consider a controlproblem where the goal is to avoid escape in the presenceof large disturbances which are greater in magnitude thanthe controls by implementing a safe-set-sculpting algorithmwhich explicitly incorporates tube dynamics.

Shibabrat NaikEngineering Science and MechanicsVirginia [email protected]

Shane D. RossVirginia TechEngineering Science and [email protected]

CP6

Periodic Social Niche Construction

Social niche construction describes the creation of socialnetworks and institutions that influence individual fitness.Niche construction involves multiple timescales, includingthe relatively short time required to build a niche, and thelonger time required to learn how to build a niche. Weexplore a number of learning rules for niche constructionin relation to competition between constructing species oragents, in particular the dynamics of institutional switch-ing, as the system undergoes a Hopf-bifurcation. Hysteresisin key competition parameters provides evidence of top-down causal memory from the institutions, leading to in-creased resistance to change between states. This is due tothe different stability criteria for a periodic solution as dic-tated by Floquets theory. We also find evidence for greaterstability in a two-institution than a single institution set-ting. We relate these results to prior discussion of stabilityinduced in bi-polar versus unipolar social systems.

Philip PoonDepartment of [email protected]

David Krakauer, Jessica FlackCenter for Complexity & Collective ComputationWisconsin Institute for [email protected], [email protected]

CP6

Experimental Verification of Criteria for Escapefrom a Potential Well in a Multi-degree of Free-

DS15 Abstracts 95

dom System

Criteria and routes of escape from a potential well havepreviously been determined for 1 degree of freedom (DOF)mechanical systems with time-varying forcing, with rea-sonable agreement with experiments. When there are 2 ormore DOF, the situation becomes more complicated, butthere is still a method, tube dynamics, for determining thephase space states which will escape. Here, we verify tubedynamics for a 2 DOF experiment of a ball rolling on asurface.


Amir BozorgMaghamUniversity of Maryland, College [email protected]

Lawrence VirginCntr for Nonlinear and Complex SystemsDuke [email protected]

CP6

Sensitivity of the Dynamics of the GeneralRosenzweig-MacArthur Model to the Mathemati-cal Form of the Functional Response: a BifurcationTheory Approach

We revisit the Rosenzweig-MacArthur predator-prey modelto help explain sensitivity to the mathematical forms ofthree functional responses (Holling type II, Ivlev, andTrigonometric). We consider both local and global dy-namics and determine possible bifurcations with respectto variation of the carrying capacity of the prey. We pro-vide an analytic expression that determines the criticalityof a Hopf bifurcation and revisit the ranking of the func-tional responses, according to their potential to destabilizethe dynamics of the model.

Gunog SeoColgate [email protected]

Gail WolkowiczMcMaster [email protected]

CP7

Numerical Simulations of Nonlinear Dynamics ofBeams, Plates, and Shells

Solution of nonlinear structural dynamics poses a challeng-ing problem and often requires the use of computers in or-der to obtain a quantitative solution. Such simulationsare usually computationally expensive and are typicallyperformed only as academic research. The current studyserves two purposes: i) it presents simple semi-implicit nu-merical formulations, which are computationally efficient,simple to use, and can be used in nonlinear dynamics andchaos simulations ii) it serves as a good introduction to nu-merical studies of nonlinear structural dynamics for grad-uate students and upper division undergraduate students.Numerical formulations along with results are presented fornonlinear oscillators, beams, von Karman plates, and thin

shells.

Timur AlexeevUniversity of California, [email protected]

CP7

A New Mathematical Explanation of What Trig-gered the Catastrophic Torsional Mode of theTacoma Narrows Bridge

We suggest a mathematical model for the study of the dy-namical behavior of suspension bridges which provides anew explanation for the appearance of torsional oscillationsduring the Tacoma collapse.

Gianni ArioliDipartimento di MatematicaPolitecnico di [email protected]

CP7

Global Attractors for Quasilinear Parabolic-Hyperbolic Equations Governing Longitudinal Mo-tions of Nonlinearly Viscoelastic Rods

We prove the existence of a global attractor and estimateits dimension for a general family of third-order quasilinearparabolic-hyperbolic equations governing the longitudinalmotion of nonlinearly viscoelastic rods subject to interest-ing body forces and end conditions. The simplest versionof the equations has the form wtt = n(wx, wxt)x where nis defined on (0,∞) × R and is a strictly increasing func-tion of each of its arguments, and with n → −∞ as itsfirst argument goes to 0. This limit characterizes a totalcompression, a source of technical difficulty, which delicatea priori estimates prevent. (These estimates simplify andgeneralize earlier versions.) We determine how the dimen-sion of the attractor varies with the several parameters ofthe problem, giving conditions ensuring that it is small.These estimates illuminate asymptotic analyses of the gov-erning equation as parameters approach limits.

Suleyman UlusoyZirve [email protected]

Stuart S AntmanUniversity of [email protected]

CP7

Revision on the Equation of Nonlinear Vibrationof the Cable with Large Sag

The problem in the conventional cable theory about therelation between the chord-line component of dynamicalcable tension and the deflection is discussed. The expres-sion of the chord-line component of dynamical cable tensionis rationally revised based on the proposed compatibilityequation. The equation of motion of cable in time andspace is then formulated with the corrected expression ofchord-line component of cable internal force and reduced tononlinear multi-degree-of-freedom system with Galerkin’smethod. Some numerical results are presented and dis-cussed. The upper limit of the sag-span ratio for which theconventional equation of cable motion can give acceptable

96 DS15 Abstracts

results is investigated.

Kun WangUniversity of [email protected]

CP7

Control Strategies for Electrically Driven Flappingof a Flexible Cantilever Perturbed by Low SpeedWind

Control parameters for the effect of low speed wind per-turbations to the electrically driven flapping of a flexiblecantilevered beam are studied both experimentally and nu-merically. The experiments consist of varying the appliedpotential (1kV-9kV) between the gap (15mm-35mm) sep-arating a conducting plastic cantilever and a rigid groundelectrode. Other inputs are the frequency (1Hz-8Hz), theinput signal type (sine, square and triangle) and windspeed (1mph-8mph). Numerical data is produced usingthe dynamic Euler-Bernoulli beam equation with viscousdamping and gravitational effects. The electrical load ap-pears as a non-linear term in the otherwise linear equation.The numerical and experimental data for the effects of elec-trical load, frequency and wind speed on vibrational am-plitude of the cantilever will be used to introduce controlstrategies for these systems.

Thomas WardDepartment of Mechanical and Aerospace EngineeringNC State [email protected]

CP8

Coexistence of Multiannual Attractors in a DiseaseInteraction Model: Whooping Cough Revisited

Incidence of whooping cough (WC) exhibits variable dy-namics with periodicity 2-5 years. We propose an alterna-tive model of WC as interacting strains via age-dependentconvalescence. The model exhibits several stable multi-annual coexisting attractors. Also, perturbation due tocase-importation and noise in transmission switches thesystem from one dynamical regime to the other. This studysuggests that variable dynamics of WC could be an emer-gent property of the interacting system, which is not ob-served earlier.

Samit BhattacharyyaNBHM, DAE, Research FellowDepartment of Pure Mathematics, University of [email protected]

Matthew Ferrari, Ottar BjornstadPenn State [email protected], [email protected]

CP8

Examining Ebola Transmission Dynamics andForecasting Using Identifiability and Parameter Es-timation

The ongoing Ebola epidemic in West Africa is larger thanall previous Ebola outbreaks combined. Here I will dis-cuss our ongoing work developing mathematical models ofthe Ebola epidemic, using a range of identifiability andparameter estimation approaches. We used these mod-els to examine uncertainty in forecasting disease dynam-

ics, and evaluated a range of questions involving spatialspread, alternative intervention strategies, and contribu-tions to transmission by different infectious stages (early-stage, late-stage, and funeral transmission).

Marisa EisenbergUniversity of [email protected]

CP8

How Radiation-Induced Dedifferentation Influ-ences Tumor Hierarchy

Evidence indicates solid tumors exhibit cellular hierarchywhere only a fraction of cells are able to maintain and re-grow the tumor. Recent discoveries indicate that, besidesthese inherent cancer stem cells, other cells can dediffer-entiate to a stem-like state after radiation exposure. Wemodify an ODE lineage model to include feedback, radia-tion, and dedifferentiation. Setting parameters with exper-imental data, we observe an elevated dedifferentiation ratefor irradiated cells that can profoundly impact long-termpopulation size.

Kimberly FesselMathematical Biosciences [email protected]

John LowengrubDepartment of MathematicsUniversity of California at [email protected]

CP8

Order Reduction and Efficient Implementation ofNonlinear Nonlocal Cochlear Response Models

The cochlea is shown to exhibit active nonlinear spatiotem-poral response dynamics. To model such phenomena, itis often necessary to incorporate cochlear fluid-membraneinteractions. This results in both high-order model formu-lations and computationally-intensive solutions that limittheir practical use (for psychoacoustic audio signal pro-cessing) even for simple single-tone brief inputs. In thispaper, we reformulate an existing nonlinear cochlear modelinto sparse state-space (SS) models that are of considerablylower order (factor of 8) and are computationally simpler(factor of 25) with little reduction in accuracy.

Maurice G. FiloPhD Student at UC Santa [email protected]

CP8

Periodic Outbreaks in Models of Disease Transmis-sion with a Behavioral Response

Recently there has been increasing interest in the effectsof behavioral responses to information on outbreaks of in-fectious diseases. Such a response can drive the infectionto low endemic levels even if it wanes over time and theinfection does not confer immunity upon recovery. Thistalk will report on recent results on the question whethera waning behavioral response provides sufficient protectionagainst subsequent flare-ups of the infection.

Winfried JustDepartment of MathematicsOhio University

DS15 Abstracts 97

[email protected]

Joan SaldanaDepartament d’Informatica, Matematica Aplicada iEstadsticaUniversitat de [email protected]

CP8

Competition and Invasion of Dengue Viruses inVaccinated Populations

The complex competitive landscape that exists between thefour dengue serotypes will change in unforeseeable wayswith the soon-to-be released commercial vaccines. Here,we use a compartmental dengue transmission model in-corporating mass vaccination to investigate the possibilityof serotype reintroduction in locations where one or moreserotypes are absent. We show that the widespread appli-cation of fully sterilizing vaccines can have the unintendedeffect of facilitating the reintroduction of missing serotypes.

Luis Mier-y-Teran, Isabel Rodriguez-BarraquerJohns Hopkins Bloomberg School of Public [email protected], [email protected]

Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]

Derek CummingsJohns Hopkins Bloomberg School of Public [email protected]

CP9

C∞ Regularisation of Local Singularities of FilippovSystems

We study the Sotomayor-Teixeira regularization of a gen-eral visible fold singularity of a Filippov system. In the casethat the regularized system is Cp−1 the deviation from the

Fenichel manifold is O(εp

2p−1 ). We extend these results tothe case where the regularized vector field is analytic. Inthis case the regularized vector field and the Filippov oneare different in the whole phase space, but this is just atechnical problem that will not change the final result.

Carles BonetUniversitat Politecnica de [email protected]

Tere M. Seara-AlonsoUniversitat Politecnica de [email protected]

CP9

Filippov Unplugged - Part 2

Following on from Filippov Unplugged part 1, we willpresent results from ”Differential equations with discon-tinuous righthand sides” that hold in n-dimensional nons-mooth systems. Focussing on issues of topological equiva-lence and structural stability, we will identify basic topo-logical classes of singularities that can occur, as well as thebifurcations that ensue. Practical examples, rooted in real

applications, will be given to illustrate the talk.

John HoganBristol Centre for Applied Nonlinear MathematicsDepartment of Engineering Mathematics, University [email protected]

Martin HomerUniversity of BristolDepartment of Engineering [email protected]

Mike R. Jeffrey, Robert SzalaiUniversity of [email protected], [email protected]

CP9

Filippov Unplugged — Part 1

Almost every paper on nonsmooth systems references thebook by Filippov “Differential equations with discontinu-ous righthand sides’ (Kluwer, 1988). The aim of this talk isto direct attention toward results therein that are relevantto the modern audience, yet do not appear to be widelyknown. In particular, we will focus on two-dimensionalflows, and discuss how we must fundamentally revise ournotions of singularities, codimension, separatrices, struc-tural stability, topological equivalence and bifurcations.


Martin HomerUniversity of BristolDepartment of Engineering [email protected]

Mike R. Jeffrey, Robert SzalaiUniversity of [email protected], [email protected]

CP9

On the Use of Blow Up to Study Regularizations ofSingularities of Piecewise Smooth Dynamical Sys-tems

This talk will demonstrate the use of the blow up methodof Krupa and Szmolyan to study the regularization of sin-gularities of piecewise smooth dynamical systems. We willprimarily focus on the regularization of the two-fold bi-furcation and the perturbation of associated limit cycles,pseudo-equilibria, and canard-like orbits connecting stablesliding with unstable sliding. We will also present resultson how the regularization function can introduce additionalbifurcation.

Kristian Uldall KristiansenTechnical University of DenmarkDepartment of Applied Mathematics and [email protected]

John HoganBristol Centre for Applied Nonlinear Mathematics

98 DS15 Abstracts

Department of Engineering Mathematics, University [email protected]

CP10

Curve Evolution in Second-Order Lagrangian Sys-tems

A second-order Lagrangian system is a generalization of aclassical mechanical system for which the Lagrangian ac-tion depends on the second derivative of the state variable.Recent work has shown that the dynamics of such systemscan be substantially richer than for classical Lagrangiansystems. In particular, topological properties of the planarcurves obtained by projection onto the lower-order deriva-tives play a key role in forcing certain types of dynamics.However, the application of these techniques requires ananalytic restriction on the Lagrangian that it satisfy a twistproperty. Here we approach this problem from the pointof view of curve shortening in an effort to remove the twistcondition.We prove the existence of simple periodic solu-tions for a general class of systems without requiring thetwist condition. Further, our results provide a frameworkin which to try to further extend the topological forcingtheorems to systems without the twist condition.

Ronald AdamsFlorida Atlantic [email protected]

William D. KaliesFlorida Atlantic UniversityDepartment of Mathematical [email protected]

R.C.A.M van Der VorstVrije [email protected]

CP10

Tensor of Green of Coupled Thermoelastodynamics

Some problems of coupled thermoelastodynamics are con-sidered. Method of boundary integral equations is used forsolution of system of integral equations, fundamental ten-sors of stresses received by using of apparate of generalizedfunctions.

Bakhyt AlipovaUniversity of [email protected]

CP10

Periodic Eigendecomposition and Its Applicationin Nonlinear Dynamics

As an extension of periodic Schur decomposition, periodiceigendecomposition is capable of calculating Floquet spec-trum and Floquet vectors along periodic orbits in chaoticsystems accurately. Its effectiveness, and in particular itsability to resolve eigenvalues whose magnitude differs byhundreds of orders, is demonstrated by applying the algo-rithm to computation of the full linear stability spectrum ofperiodic solutions of Kuramoto-Sivashinsky system. Also,its efficiency is compared with the existing covariant vec-tors algorithm.

Xiong Ding

School of Physics, Georgia Institute of [email protected]

Predrag CvitanovicCenter for Nonlinear ScienceGeorgia Institute of [email protected]

CP10

Error Assessment of the Local Statistical Lineariza-tion Method

We determine probability density functions of multidimen-sional stochastic differential equations by means of theLocal Statistical Linearization method. The core of thismethod is the approximation of a non-Gaussian probabil-ity density by superposition of Gaussian densities. For this,the evolutions of local Gaussian densities are calculatedand used in a time stepping scheme. Moreover, we provideerror evolutions using accurate Monte Carlo simulations,Stochastic Averaging and available analytical solutions.

Leo DostalHamburg University of TechnologyInstitute of Mechanics and Ocean [email protected]

Edwin KreuzerInstitute of Mechanics and Ocean EngineeringHamburg University of [email protected]

CP10

Geometric Phase in the Hopf Bundle and the Sabil-ity of Non-Linear Waves

Building on the Evans function, we have proven a related,alternative form of analysis that uses the Hopf bundle todetermine the stability of traveling waves. The total spaceof the Hopf bundle is S2n−1 and it is naturally embedded inCn. The dynamical system associated with the linearizedoperator for a PDE induces a winding number through par-allel transport in the fibre, S1. Our method uses paralleltransport to count the multiplicity of eigenvalues.

Colin J. GrudzienUniversity of North Carolina at Chapel HillMathematics [email protected]

Christopher Krt JonesUniversity of North Carolina at Chapel [email protected]

CP10

Computation of Cauchy-Green Strain Tensor UsingLocal Regression

The Cauchy-Green strain tensor provides an effective toolfor understanding unsteady flows. We propose a newmethod for computing the CG strain tensor using a localquadratic regression (LOESS) technique. We compare thisLOESS method with several classical methods using closedform flows, noisy flows, and simulated time series. In eachcase the CG strain tensor produced by the LOESS methodis remarkably accurate and robust compared to classical

DS15 Abstracts 99

methods.

Shane D. KepleyFlorida Atlantic [email protected]

Bill KaliesFlorida Atlantic UniversityDepartment of Mathematical [email protected]

CP11

Odd-Number Limitation for Extended Time-Delayed Feedback Control

Time-delayed feedback control is a simple and estab-lished method to stabilize unstable periodic orbits withina chaotic attractor. Here we prove a generalization of thewell-known odd-number limitation of this control methodto the case of autonomous systems. This result is furthergeneralized to the extended version of time-delayed feed-back control. We uncover the important role played bythe period of the orbit that is induced by mismatching thedelay time of the control scheme.

Andreas Amann, Edward HootonSchool of Mathematical SciencesUniversity College [email protected], [email protected]

CP11

Approximate Controllability of An Impulsive Neu-tral Fractional Stochastic Differential EquationWith Deviated Argument and Infinite Delay

We proved the approximate controllability of an impul-sive fractional stochastic neutral integro-differential equa-tion with deviated argument and infinite delay. We usedSchauder fixed point theorem and fundamental assump-tions on system operators. The inverse of controllabilityoperator fails to exist in infinite dimensional space in casegenerated semigroup is compact. Therefore, the need toassume the invertibility of controllability operator is re-moved. Lipschitz continuity is also not required. Specif-ically we studied the following remote control dynamicalsystem

cDqt [x(t) + g(t, xt)] = A[x(t) + g(t, xt)] +Bu(t) + f(t, x(a(x(t), t)), u(t))

+

∫ t

−∞G(xs)dW (s), t ∈ J = [0, T ], t �= tk, k = 1, ..., m

x0(t) = φ(t), t ∈ J1 = (−∞, 0]

x(t+k )− x(t−k ) = Ik(x(tk)), k = 1, ..., m,

Sanjukta DasIndian Institute of Technology, Roorkee,sanjukta [email protected]

Dwijendra PandeyIndian Institute of Technology, [email protected]

CP11

Chaos in Biological Systems with Memory and ItsControllability

Biological systems, a neuron, the brain, the heart, a human

being, a society .., are systems with memory (in many casespower-law). This implies a possibility of their descriptionby fractional differential equations or maps with power-law memory. Nonlinear systems with power-law memorydemonstrate new features, including cascade of bifurca-tions type behavior (with fixed parameters). This behav-ior could be related to the evolution of chronic diseases,epileptic seizures, and evolution of the human society. Innonlinear systems with power-law memory chaos can becontrolled by changing nonlinearity parameter and also bychanging a memory parameter of a system.

Mark EdelmanStern College for Women and Courant [email protected]

CP11

Discrete-Time Structure-Preserving Optimal Er-godic Control

Trajectories are ergodic with respect to a measure whenthe amount of time spent in a neighborhood is propor-tional to the measure evaluated over the neighborhood,making ergodicity an appropriate metric for searching a do-main. Ergodic control in higher dimensional configurationspaces requires discretization of the optimal control formu-lation. Recent works have shown advantages of structure-preserving variational integrators in control and estimationof mechanical systems. Here we develop a discrete-timevariational optimal ergodic control scheme.

Kathrin Flakamp, Todd MurpheyNorthwestern [email protected], [email protected]

CP11

Mathematical Study of the Effects of Travel Costson Optimal Dispersal in a Two-Patch Model

How might organisms constrained by perceptual limita-tions or imperfect information use resource information op-timally in habitat selection? We analyze a general ordinarydifferential equation model of a single species in a two-patch heterogeneous environment. Global stability analy-sis yields an evolutionarily stable information use strategythat depends on the magnitude of the constraints and theheterogeneity of the resources. Incorporating travel costsinto the model yields a different strategy that is locallyconvergent stable

Theodore E. GalanthayUniversity of [email protected]

CP11

Computing Bisimulation Functions Using SoS Op-timization and δ-Decidability over the Reals

We present BFComp, an automated framework basedon Sum-Of-Squares (SOS) optimization and δ-decidabilityover the reals to compute Bisimulation Functions (BFs)that characterize input-to-output stability (IOS) of dynam-ical systems. BFs are Lyapunov-like functions that decayalong the trajectories of a given pair of systems, and canbe used to establish the stability of the outputs with re-spect to bounded input deviations. In addition to estab-lishing IOS, BFComp is designed to provide tight boundson the squared output errors between systems whenever

100 DS15 Abstracts

possible. For this purpose, two SOS optimization formu-lations and δ-decidability-based Satisfiability Modulo The-ory are employed. We illustrate the utility of BFComp on afeedback-based canonical cardiac-cell model, showing thatthe four-variable Markovian model for the slow Potassiumcurrent IKs can be safely replaced by an approximatelyone-variable Hodgkin-Huxley-type approximation.

Abhishek MurthyPhilips Research North [email protected]

Md. Ariful Islam, Scott SmolkaComputer ScienceStony Brook [email protected], [email protected]

Radu GrosuVienna University of [email protected]

CP12

Empirical Validation of Conceptual Climate Mod-els

Conceptual climate models are useful for testing hypothe-ses regarding the processes underlying observations; butthey generally can only qualitatively match the empiricalrecords. Models based on substantially different underlyingphysics can have comparable correlations with any givenobservation; more robust model validation procedures areneeded. Using the Mid-Pleistocene Transition as a testcase, we will show how modern time-series-analysis tech-niques can improve validation by extracting subtler fea-tures of the observations and models.

Charles D. Camp, Ryan Smith, Andrew GallatinCalifornia Polytechnic State [email protected], [email protected], [email protected]

CP12

Modified Lorenz Equations for Rotating Convec-tion

We derive and examine systems of nonlinear differentialequations similar to the Lorenz equations. In particu-lar, starting from the partial differential equations describ-ing two-dimensional Rayleigh-Benard convection we derivesystems of ordinary differential equations that are slightmodifications of Lorenz’ original system. These new sys-tems of equations incorporate the effects of rigid body ro-tation. We investigate the role that rotation has on thedynamics of these reduced models.

Jessica [email protected]

Jared P. Whitehead, Shane McQuarrieBrigham Young [email protected],[email protected]

CP12

On the Geometry of Attractors in Ageostrophic

Flows with Viscoelastic-Type Reynolds Stress

Progress utilizing other closure protocols appear in thisresearch and innovation. Although this article is moti-vated by challenges in partial differential equations, weconsider a two-mode Faedo-Galerkin approximation(EdLorenz ansatz sense) given by a system of singularly per-turbed ordinary differential equations in R4:

RodX

dt= Y − EkX − λEkW,

dY

dt= εX +X − Y −XZ,

dZ

dt= −bZ +XY,

WedW

dt= r(δλX −W ).

It is shown that the equilibrium point at the origin isasymptotically stable and attractive by the LaSalle in-variance principle. Utilizing center manifold calculations,we show existence of supercritical pitchfork bifurcationand Poincare-Andronov-Hopf bifurcation. In order to uti-lize geometric singular perturbation theory and Melnikovtechniques, we perturb the problem and carry the non-linear analysis further to the question of the persistenceof inclination-flip homoclinic solutions. We present a geo-metric approach to the problem which gives more refined apriori energy type estimates on the position of the invari-ant manifold and its tangent planes as the manifold passesclose to a normally hyperbolic piece of a slow manifold.The main object of this result enables detection of chaoticattractors in singularly perturbed dynamical systems as de-picted using the DsTool(Dynamical systems Tool) packageprogram of Worfolk et al.

Maleafisha Stephen TladiUniversity of Limpopo, South [email protected]

CP12

Baroclinic Instability in An Initially Stratified Ro-tating Fluid

Motivated by the large-scale atmospheric and oceanic cir-culation, we study the characteristics of density-driven con-vective flow in an annular, tabletop-size rotating laboratorytank, filled with water. Horizontal and vertical density gra-dients are induced by differential heating at the sidewallsand salinity stratification, respectively. These boundaryconditions, together with the rotation of the tank, yieldan interesting interplay between double-diffusive convec-tion and baroclinic instability.

Miklos P. VinczeHAS ELTE Theoretical Physics Research [email protected]

Patrice Le GalIRPHE, CNRS-Aix [email protected]

Uwe HarlanderBTU Cottbus, Department of Aerodynamics and FluidMechanics

DS15 Abstracts 101

[email protected]

CP12

Gradual and Abrupt Regime Shifts in Drylands

The response of ecosystems to climatic changes and an-thropogenic disturbances are crucial to our understandingof these systems. Transitions in drylands due to these per-turbations may take various forms, in particular due to thepatterned nature of patchy vegetation. I will discuss mul-tistability in these systems, owing to localized states andpatterns with various wavelength, and possible transitionsin them. A case study of fairy circles in Namibia will bepresented as a concrete example.

Yuval ZelnikBen-Gurion University of the [email protected]

Ehud MeronBen-Gurion [email protected]

Golan BelDepartment of Solar Energy and Environmental PhysicsBen-Gurion [email protected]

CP13

Localized States in Periodically Forced Systems

The generalized Swift–Hohenberg equation with aquadratic-cubic nonlinearity is used to study localized pat-tern formation in the presence of time-periodic parametricforcing. Regions of parameter space with distinct dynam-ics result from resonances between the period of the forcingand the time it takes the state to nucleate/annihilate wave-lengths of the pattern. The non-trivial structure of theseregions can be understood qualitatively, and in some casesquantitatively, by asymptotic arguments.

Punit R. GandhiDepartment of PhysicsUniversity of California, Berkeleypunit [email protected]

Cedric BeaumeImperial College [email protected]

Edgar KnoblochUniversity of California at BerkeleyDept of [email protected]

CP13

Multicluster and Traveling Chimera States in Non-local Phase-Coupled Oscillators

We study a nonlocal phase-coupled oscillator model inwhich chimera states develop from random initial condi-tions. Several classes of chimera states have been found:(a) stationary multi-cluster states with evenly or unevenlydistributed coherent clusters (b) a coherent state travelingwith a constant speed or in a stick-slip fashion (c) chimerastates traveling with a constant speed. A self-consistentcontinuum description of these states is provided and theirstability properties are analyzed through a combination of

linear stability analysis, numerical continuation, and di-rect numerical simulation. Heterogeneities in the naturalfrequency of the oscillators select the location of the co-herent clusters and may lead to their breakup. Pinning oftraveling states by heterogeneities may occur, followed bydepinning as the heterogeneity decreases.

Hsien-Ching KaoWolfram Research [email protected]

Jianbo XieDepartment of PhysicsUniversity of California at [email protected]


CP13

Chimera States on the Route from Coherent Stateto a Rotating Wave

We discuss the occurrence of chimera states on the routefrom coherent via solitary states to the rotating wave inthe networks of non-locally coupled pendulum-like nodes.We identify the wide region in parameter space, in whicha new type chimera state, imperfect chimera state, whichis characterized by a certain number of oscillators escapedfrom synchronized chimeras cluster appears. We describe anovel mechanism for the creation of chimera states via theappearance of the so-called solitary states. Our findings re-veal that imperfect chimera states represent characteristicspatio-temporal patterns at the transition from coherenceto incoherence.

Tomasz KapitaniakTechnical University of LodzDept of [email protected]

CP13

Emergent Rhythmic Behavior of Mixed-Mode Os-cillations in Pulse-Coupled Neurons

Our study is motivated by the experimental observationof fast and slow rhythms in the mammalian olfactory sys-tem. We develop a minimal model in which the interac-tion of three relevant populations of neurons is reduced toan effective pulse-coupling within a single population ofmixed-mode oscillators. This pulse-coupling features mul-tiple pulses with distinct propagation delays. We explorethe dynamics of the system as a function of the shapes anddelays of the pulses.

Avinash J. KaramchandaniDepartment of Engineering Sciences and AppliedMathematicsNorthwestern [email protected]

James GrahamNorthwestern [email protected]

Hermann RieckeApplied Mathematics

102 DS15 Abstracts

Northwestern [email protected]

CP13

Onset and Characterization of Chimera States inCoupled Nonlinear Oscillators

Role of symmetry breaking in nonlocal and global couplingsof networks of identical nonlinear oscillators for the occur-rence of chimera mediated transitions between desynchro-nized and synchronized states will be discussed. We willalso distinguish between amplitude chimera and frequencychimera states in this process and identify the conditionsunder which chimera death states can arise. New rigorousquantitative measures to distinguish the above collectivestates in terms of strength of incoherence and discontinu-ity measure will be presented.

Lakshmanan MuthusamyCentre for Nonlinear Dynamics, Department of PhysicsBharathidasan University, Tiruchirapalli 620024, [email protected]

CP14

Reduced Modeling of Exact Coherent States inShear Flow

In parallel shear flows, the lower branch solution followssimple streamwise dynamics. A decomposition of this so-lution into Fourier modes in this direction yields modeswhose amplitudes scale with inverse powers of the Reynoldsnumber. We use this scaling to derive a reduced model forexact coherent structures in general parallel shear flows.The reduced model is regularized by retaining higher or-der viscous terms. Both lower branch and upper branchsolutions are captured and studied.

Cedric BeaumeImperial College [email protected]

Greg ChiniProgram in Integrated Applied MathematicsUniversity of New [email protected]

Keith JulienApplied MathematicsUniversity of Colorado, [email protected]


CP14

Stratified Shear Turbulence Experiments

We report experiments on stratified wall-bounded shearflows in which we determine both the velocity and densityfields. The flows undergo Kelvin-Helmholtz and Holmboeinstabilities depending on the strength of the stratificationand shear. We characterize the instabilities by the Richard-son number dependence of a local Thorpe length that de-fines an intermittency fraction for the density interface andallows for an evaluation of the probability distribution of

Thorpe length. We discuss applications to ocean overflows.

Robert E. EckeCenter for Nonlinear StudiesLos Alamos National [email protected]

Philippe OdierENS [email protected]

CP14

Effects of Fluid Dynamics on Experiments withCompressed/ Expanded Surfactant Monolayers

Monolayer experiments frequently measure surface rheo-logical properties by periodically modulating surfactantconcentration with two slightly immersed solid barriersthat control the free surface area of a shallow liquid layer.Because the modulation is slow, most theoretical studiesignore fluid dynamics in the bulk. We present a long wavetheory that also takes fluid dynamics and symmetries intoaccount. A nonlinear diffusion equation for surfactant con-centration that includes free surface deformation showsthat fluid dynamics can be an important source of irre-versibility and help explain experimental observations.

Maria HigueraE. T. S. I. AeronauticosUniv. Politecnica de [email protected]

Jose PeralesE. T. S. I. AeronauticosUniversidad Politecnica de [email protected]

Jose VegaE. T. S. I. AeronauticosUniversidad Politecnica de [email protected]

CP15

Noisy-Bar Problem

We have all experienced the inability to hear and under-stand our conversation partner in a crowded room. Thedifficulty tends to be most apparent in a crowded bar or aclub setting. Aside from presenting a social inconvenience,this problem is also closely connected to the issue of signalto noise ratio in networked electronics. In this talk I willpresent a simple dynamical systems model that explainsthe transition from a quiet to loud environment.

Korana BurkeUC [email protected]

CP15

Embedology for Control and Random DynamicalSystems

We introduce a data-based approach to estimating keyquantities which arise in the study of nonlinear controlsystems and random nonlinear dynamical systems. Ourapproach hinges on the observation that much of the ex-isting linear theory may be readily extended to nonlinearsystems - with a reasonable expectation of success- once the

DS15 Abstracts 103

nonlinear system has been mapped into a high or infinitedimensional reproducing kernel Hilbert space. In particu-lar, we embed a nonlinear system in a reproducing kernelHilbert space where linear theory can be used to developcomputable, nonparametric estimators approximating con-trollability and observability energy functions for nonlinearsystems, and study the ellipsoids they induce. It is thenshown that the controllability energy estimator providesa key means for approximating the invariant measure ofan ergodic, stochastically forced nonlinear system. In allcases the relevant quantities are estimated from simulatedor observed data.

Boumediene HamziImperial CollegeDepartment of [email protected]

Jake [email protected]

CP15

Faster Sensitivity Estimates for Stochastic Differ-ential Equations

Estimating the sensitivity of model predictions to param-eter variations is a common task in scientific computing.When the model in question takes the form of a stochasticdifferential equation, sensitivity estimates can be compu-tationally expensive, particularly if the system at hand ischaotic. In this talk, I will describe a class of algorithmsfor speeding up sensitivity estimates for models of noisy,chaotic systems.

Kevin K. LinDepartment of MathematicsUniversity of [email protected]

Jonathan C. MattinglyDuke [email protected]

CP15

Noise Shaping and Pattern Discrimination in Re-current Spiking Neuronal Networks

The enhancement of pattern discrimination is considered acommon step in early sensory processing by the brain, oftenattributed to a recurrent network. It has been suggestedthat noise correlations arising from the common feedbackwithin recurrent spiking networks may interfere with theintended pattern discrimination. We show that recurrentexcitatory-inhibitory networks with reciprocal connections,as they arise in the olfactory system, can reshape the noisesuch that the network can enhance pattern discriminabilityefficiently.

Hermann RieckeApplied MathematicsNorthwestern [email protected]

Tom Zhao, Siu Fai ChowNorthwestern [email protected], siu-

[email protected]

CP15

Zero Density of Open Paths in the Lorentz MirrorModel for Arbitrary Mirror Probability

The Lorentz mirror model consists of a particle bounc-ing off randomly-oriented mirrors placed at integer latticepoints, and is thus a key model of deterministic dynamicsin a quenched random environment. We will present effi-cient numerical simulations to count closed and open pathsin the Lorentz mirror model, and arguments based on theresults of those simulations [A.S. Kraemer & D.P. Sanders,Journal of Statistical Physics 156, 908–916], to show thatthe density of open paths in a finite box tends to 0 as thebox size tends to infinity, for any probability p > 0 of plac-ing a mirror at a point.

David P. SandersDepartment of Physics, Faculty of SciencesNational University of Mexico (UNAM)[email protected]

Atahualpa KraemerHeinrich-Hein University of [email protected]

CP15

Power System Stochastic Modeling

We develop and test recent methods in power systems sim-ulation. A stochastic Runge-Kutta single-step solver is pro-posed; error coefficients and order conditions are derived.A new method of retrieving the algebraic system variablesafter topological changes (i.e. line tripping) in the modelsystem is examined. The stability behavior of the systemis studied under stochastic forcing and topological distur-bances.

Mathew Titus, Yue Zhang, Eduardo Cotilla-SanchezOregon State [email protected],[email protected],[email protected]

CP16

Effects of Network Structure on the Synchroniza-tion of Hamiltonian Systems

Hamiltonian systems exhibiting long-range interactions arefrequently modeled using the Hamiltonian Mean Field(HMF) model. Past research on the HMF has focused onthe all-to-all case where each rotor is connected to everyother rotor. We study the HMF on complex networks ofinteractions amongst the rotors. We find that althoughthe network structure impacts the onset of rotor synchro-nization and the path to synchrony, the maximum possiblesynchrony is fairly independent of network structure.

Yogesh VirkarDepartment of Computer ScienceUniversity of Colorado, [email protected]

Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]

104 DS15 Abstracts

James D. MeissUniversity of ColoradoDept of Applied [email protected]

CP16

Transient Spatiotemporal Chaos in a Network ofCoupled Morris-Lecar Neurons

Spatiotemporal chaos collapses to either a rest state or apropagating pulse solution in a ring network of diffusivelycoupled, excitable Morris-Lecar neurons. The addition ofweak excitatory synapses can increase the Lyapunov expo-nent, expedite the collapse, and promote the collapse tothe rest state rather than the pulse state. A pulse solutionmay no longer be asymptotic for certain network topologiesand (weak) synapses.

Renate A. WackerbauerUniversity of Alaska FairbanksDepartment of [email protected]

Jacopo LafranceschinaUniversity of Alaska [email protected]

CP16

Consequence of Symmetry Breaking in Two Cou-pled Kuramoto Networks

We explore symmetry breaking in a two-population Ku-ramoto network, using the ansatz of Ott and Antonsen[Chaos 18, 037113 (2008)]. We find that the systemis a generalized formulation for a single population ofsymmetrically-coupled, bimodally-distributed oscillators.We explore this systems equilibria and invariant sets andcharacterize the bifurcations of both the incoherent andpartially-coherent states. We then identify and break sev-eral symmetries present in this system, to see how the dy-namics change.

Scott T. WatsonGeorge Mason [email protected]

Ernest BarretoGeorge Mason UniversityKrasnow [email protected]

Bernard CottonGeorge Mason [email protected]

Paul SoGeorge Mason UniversityThe Krasnow [email protected]

CP16

Control of Stochastic and Induced Switching inBiophysical Complex Networks

While the response of biological systems to noise has beenstudied extensively, there has been limited understand-ing of how to exploit these fluctuations to induce a de-sired cell state. Here we present a method based on

the Friedlin-Wentzell action to predict and control noise-induced switching between different attracting states in ge-netic regulatory networks. We utilize this methodology toidentify new candidate strategies for cancer therapy in acoupled ODE model of the cell death pathway.

Daniel WellsNorthwestern UniversityDepartment of Engineering Sciences and [email protected]

William KathDepartment of Applied Mathematics, NorthwesternUniversityDepartment of Neurobiology, Northwestern [email protected]

Adilson E. MotterNorthwestern [email protected]

CP16

Studies of Stable Manifolds of a Spatially ExtendedLattice Kuramoto Model

We study the steady state solution of the 1D and 2Dspatially extended Kuramoto model with nearest-neighborcoupling for a range of system sizes. Past the critical cou-pling σc, different possible steady states can appear includ-ing phase coherence (synchronization), and phase locking(traveling wave states). We characterize the terminal be-havior of a space of initial conditions for a variety of bound-ary conditions: periodic, zero-flux and free.

Andrea J. Welsh, Flavio FentonGeorgia Institute of [email protected], [email protected]

CP17

Efficient Kernel Algorithm for the Dynamic ModeDecomposition of Observed Data

The dynamic mode decomposition (DMD) is a recentlyproposed algorithm for decomposing time series data ob-served from nonlinear dynamical systems. We extend theDMD by using a statistical technique called the kernelmethod. Our extended DMD can compute the mode de-composition significantly faster and more accurately thanother methods. In addition, we theoretically discuss thesufficient condition for the modes to be reconstructed fromobserved time series. We illustrate the validity and useful-ness of our method by numerical examples.

Wataru Kurebayashi, Sho ShirasakaTokyo Institute of [email protected], [email protected]

Hiroya NakaoGraduate School of Information Science and Engineering,Tokyo Institute of [email protected]

CP17

Perturbing the Cat Map: Mixed Elliptic and Hy-perbolic Dynamics

Arnolds cat map is a prototypical dynamical system with

DS15 Abstracts 105

uniformly hyperbolic dynamics. We study a family of mapshomotopic to the cat map that has a saddle and a parabolicfixed point. Lerman conjectured that this map has a mixedphase space. We present some evidence in support. Theelliptic orbits are confined to a channel bounded by mani-folds of the fixed points. The complement appears to havepositive measure with positive Lyapunov exponents.


Lev LermanLobachevsky State University of Nizhny [email protected]

CP17

Invariant Manifolds and Space Mission Design inthe Restricted Four-Body Problem

Invariant manifolds play a crucial role in designing low-energy trajectories of a spacecraft. We consider the four-body problem of Sun, Earth, Moon and a spacecraft by re-garding the system as a coupled system of distinct RC3BPswith perturbations, namely, the systems of Sun-Earth-S/C+ (Moon perturb) and Earth-Moon-S/C+ (Sun per-turb). We clarify tube-like invariant manifolds of each per-turbed system and design a transfer trajectory from Earthto Moon by patching trajectories associated with the in-variant manifolds.

Kaori OnozakiWaseda [email protected]

Hiroaki YoshimuraWaseday [email protected]

CP17

Mixing on a Hemisphere

Motivated by mixing in 3D rotated granular flows, we studythe nonlinear dynamics of piecewise isometries (PWI) on ahemispherical shell for different rotation protocols. Map-pings of singularities, termed the exceptional set, E, coverthe hemisphere’s surface in a variety of complex patternsand explain the ultimate degree of mixing but not the rateof mixing. To understand the mixing rate, we explore aLyapunov exponent inspired method based on the parti-tioning property of PWI.

Paul ParkNorthwestern [email protected]

Paul Umbanhowar, Julio OttinoNorthwestern UniversityEvanston, IL [email protected],[email protected]

Richard M. LueptowNorthwestern UniversityDepartment of Mechanical Engineering

[email protected]

CP17

Classification of Critical Sets and Images forQuadratic Maps of the Plane

Real quadratic maps of the plane form a 12-parameter fam-ily and exhibit a huge range of complicated dynamics. Toconsider the whole class of maps together, we consider onlycritical sets (J0) and their images (J1). J0 is a possibly de-generate conic section. Possibilities for J1 are surprisinglyrestricted. We study this classification with a hierarchi-cal structure - first via a normal form for homogeneousquadratic maps, and then for linear perturbations of thesehomogeneous maps.

Bruce B. PeckhamDept. of Mathematics and StatisticsUniversity of Minnesota [email protected]

Chia-Hsing NienDepartment of Financial and Computational MathematicsProvidence University Taichung City 43301 [email protected]

Richard McGeheeUniversity of [email protected]

Bernd Krauskopf, Hinke M. OsingaUniversity of AucklandDepartment of [email protected], [email protected]

CP17

The Existence of Horseshoe Dynamics in Three Di-mensional Lotka-Volterra Systems

We prove the existence of horseshoe dynamics in threedimensional Lotka-Volterra systems. The proof uses aShilnikov-type structure adapted to the geometry of thethese systems.

Rizgar Salih, Colin ChristopherPlymouth [email protected],[email protected]

CP18

Inferring Causal Structures in Complex SystemsVia Causation Entropy

Perhaps the most fundamental question in science in com-plex systems is to infer causes from influences betweenmany coupled elements. Empirically inferring causal struc-ture in complex systems by means of statistical and infor-mation theoretic techniques applied to time series data is ahighly challenging and sensitive problem. We report hereon our latest results of casual coupling inferences withinthe framework of the Optimal Causation Entropy (oCSE)approach, together with example applications.

Carlo Cafaro, Warren Lord, Jie Sun, Erik BolltClarkson [email protected], [email protected],

106 DS15 Abstracts

[email protected], [email protected]

CP18

Robustness of Nonlinear Models

We propose an algorithm to test the robustness to param-eter variation of complex nonlinear models. In order tofind the minimal parameter perturbation that can destroya nominal solution, the algorithm uses numerical contin-uation techniques to move towards the closest bifurcationpoint to the nominal parameter values, then solves a con-strained optimization problem to identify the closest pointof the bifurcation manifold to the nominal parameters.

Fabio Della RossaDipartimento di Elettronica, Informazione e BioingegneriaPolitecnico di [email protected]

Alessandro ColomboPolitecnico di [email protected]

Fabio Dercole, Carlo PiccardiDipartimento di Elettronica, Informazione e BioingegneriaPolitecnico di [email protected], [email protected]

CP18

A New Filter for State Estimation in Neural MassModels

The presentation will introduce a new filter for state es-timation of neural mass models. The ability to estimateand track states in large-scale neural models is critical fordeveloping robust therapies via model-based feedback con-trol using electrical stimulation. Model-based control isparticularly important for diseases such as epilepsy, wherepathologies are highly patient-specific. The new filter issimilar to the unscented Kalman filter, where a Gaussianapproximation is used. However, the mean and covarianceof the state estimates are propagated analytically. The an-alytic results lead to an increase in estimation accuracy anda decrease in computational demands. The development ofthe new methods presented in this presentation will facili-tate the development of large-scale patient-specific compu-tational model of neurological diseases and open the doorto the possibility of novel therapies.

Dean R. FreestoneUniversity of Melbourne, Australia& The Bionics Institute, Melbourne, [email protected]

Philippa Karoly, Dragan Nesic, Mark CookThe University of [email protected],[email protected], [email protected]

David GraydenUniversity of Melbourne, Australia& The Bionics Institute, Melbourne, [email protected]

CP18

Hysteresis Effects in Pedestrian Flows

We model a crowd of pedestrians as point particles mu-

tually interacting through ’social’ forces and forces fromconstraining walls and obstacles. In counterstreaming con-stricted flows, blocking evolves through a Hopf bifurcationinto oscillatory flows. In flows around an obstacle, we findthat a simple local correlation term in the social force givesrise to hysteresis, with obstacle position as the parameter.We have performed experiments to compare with the dy-namical model.

Poul G. HjorthTechnical Univ of DenmarkDepartment of [email protected]

Jens StarkeTechnical University of DenmarkDepartment of [email protected]

CP18

Dynamics of Correlated Novelties

One new thing often leads to another. Kauffman and oth-ers have hypothesized that this correlation between novel-ties is important for understanding anything that evolves:life, technology, language, etc. Ill discuss a simple modelthat predicts the dynamical fingerprints of correlated nov-elties (they take the form of certain statistical signatures)and then test the predictions against enormous data sets ofhuman activity (listening to songs, writing words in books,making up tags, and editing Wikipedia pages).

Steven H. [email protected]

CP18

Systems with Hidden Slow Fast Dynamics

Examples of biochemical systems with complicated non-obvious slow fast structures will be presented. In suitablescalings or blow-ups hidden slow manifolds organizing thedynamics can be found and utilized in the analysis of thedynamics.

Peter SzmolyanInstitute for Analysis and Scientific ComputingVienna University of [email protected]

CP19

A Dynamical and Algebraic Study of a Family ofLienard Equations Transformable to Riccati Equa-tions

In this talk we present some algebraic and dynamical re-sults corresponding to the five parameter differential equa-tion

yy′ = (αx2k + βxm−k−1)y + γx2m−2k−1 y′ =dy

dx,

being a, b, c ∈ C, m, k ∈ Z and

α = a(2m+k)xm+k−1 β = b(2m−k)xm−k−1, γ = −(amx4k+cx2k+bm).

This equation is a foliation of a five parameter Lienardequation, which is transformed into a Riccati equation.These transformations are used to do an algebraic analy-sis about the obtaining of explicit solutions (in differential

DS15 Abstracts 107

Galois sense) of the Lienard equation, as well the obtain-ing of some elements from Darboux theory of integrability:invariant algebraic curves, first integrals, cofactors, etc..of the Lienard vector field. Finally, a qualitative analysisis presented (type of critical points, Lyapunov functions,etc..)

Primitivo B. Acosta-Humanez, JorgeRodriguez-Contreras, Alberto Reyes-LineroUniversidad del [email protected], [email protected],[email protected]

CP19

New Asymptotics of Homoclinic Orbits NearBogdanov-Takens Bifurcation Point

We derive explicit asymptotics for the homoclinic orbitsnear a generic Bogdanov-Takens (BT) point, with the aimto continue the branch of homoclinic solutions that isrooted in the BT point in parameter and state space. Wepresent accurate second-order homoclinic predictor of thehomoclinic bifurcation curve using a generalization of thePoincare-Lindstedt (P-L) method. We show that the P-Lmethod leads to the same homoclinicity conditions as theclassical Melnikov technique, the branching method andthe regular perturbation method (R-P). The R-P methodshows a “parasitic turn” near the saddle point. The newasymptotics based on P-L do not have this turn, making itmore suitable for numerical implementation. We show howto use these asymptotics to calculate the initial homocliniccycle to continue homoclinic orbits in two free parame-ters. The new homoclinic predictors are implemented inthe Matlab continuation package MatCont to initialize thecontinuation of homoclinic orbits from a BT point. Severalexamples in the case of multidimensional state spaces areincluded.

Bashir M. Al-HdaibatDept. of Applied Math., Computer Science and StatisticsGent University, [email protected]

Willy GovaertsGhent [email protected]

Yuri KuznetsovDepartment of Applied Mathematics,University of Twente, The [email protected]

Hil MeijerTwente University, [email protected]

CP19

Periodic Orbit Theory of Continuous Media

Nonlinear PDEs of a wide range, from Navier-Stokes equa-tions for viscous fluids to the Yang-Mills equations forgauge fields, can exhibit chaos. One can use high dimen-sional exact coherent solutions of these systems to predictphysical observables by utilizing trace sums over relativeperiodic orbits. These trace formulas are exact for classicalsystems, but, as we shall demonstrate on several applica-tions, their convergence can be highly nontrivial.

Nazmi Burak Budanur

School of Physics and Center for Nonlinear [email protected]


CP19

Metric Invariance Entropy and Conditionally In-variant Measures

Invariance entropy is a measure for the data rate neededto make a subset of the state space of a control systemsinvariant. Here a notion of metric invariance entropy isconstructed with respect to a conditionally invariant mea-sure for control systems in discrete time. It is shown thatthe metric invariance entropy is an invariant under conju-gations and that the topological invariance entropy (alsocalled feedback entropy) provides an upper bound.

Fritz ColoniusUniversity of [email protected]

CP19

A Fast Explicit Method for Computing InvariantSolutions of High-Dimensional Dynamical Systemswith Continuous Symmetries

Given a dynamical system with a continuous symmetry, weconstruct a perturbed system whose trajectories convergeto the invariant solutions of the original dynamical system.The perturbation term is a measure of the curvature of thetrajectories and is readily computable from the equationsof motion. The computational cost is therefore reducedconsiderably compared to algorithms based on Newton’siterations or variational methods.

Mohammad FarazmandMathematics, ETH [email protected]


CP19

Dimensionality Reduction of Collective Motion byPrincipal Manifolds

Current nonlinear dimensionality reduction methods as ap-plied to collective motion of agents may exhibit unfaithfulembedding, due to limitations of control over the map-ping between original and embedding spaces. We proposean alternative approach by minimizing the orthogonal er-ror while topologically summarizing the high-dimensionaldata. We construct embedding coordinates in terms ofgeodesic distances along smoothed principal curves, suchthat, the mapping between original and embedding spacesis defined in terms of local coordinates.

Kelum D. GajamannageClarkson [email protected]

Sachit Butail

108 DS15 Abstracts

Indraprastha Institute of Information Technology [email protected]

Maurizio PorfiriDept. of Mechanical, Aerospace and ManufacturingEngineeringPolytechnic [email protected]

Erik BolltClarkson [email protected]

CP20

On the Numerical Integration of One NonlinearParabolic Equation

In the present paper author considers initial-boundaryproblem to following nonlinear parabolic equation:

∂U

∂t=

∂

∂x

(k

(∂U

∂x

)∂U

∂x

)+f (x, t, U) , (x, t) ∈ (0, 1)×(0, T ] , T > 0.

For the mentioned problem author constructs the corre-sponding difference scheme and in certain conditions provesthe convergence of its solution to the solution of the sourceproblem with the convergence rate O

(τ + h2

). For the

same difference scheme in the same conditions the exis-tence and uniqueness of its solution is proved.

Mikheil TutberidzeIlia State UniversityAssociated [email protected]

CP20

A Continuous Model for the Pathfinding Problemwith Self-Recovery Property

We propose a model which is capable of finding a path con-necting two specified vertices which are connected by uni-directional edges. The system has a self-recovery property,i.e., the system can find a path when one of the connectionsin the existing path is suddenly terminated.

Kei-Ichi UedaFaculty of Science, University of [email protected]

Masaaki YadomeWPI-AIMR, Tohoku [email protected]

Yasumasa NishiuraRIES, Hokkaido [email protected]

CP20

Patterns on Curved Backgrounds: the Influence ofLocal Curvature on Pattern Formation

We indicate how the concepts and approaches developedin the context of the (linear) theory of patterns on flatbackgrounds (such as R2) can be extended to more generalsurfaces with nonvanishing curvature. The influence of lo-cal curvature on the appearance and dynamics of patternsis demonstrated by a number of example surfaces, where

it is clear that surface curvature can have nontrival andsurprising effects.

Frits VeermanMathematical InstituteUniversity of [email protected]

Philip K. MainiCentre for Mathematical BiologyUniversity of [email protected]

CP20

Nonlinear Behaviors As Well As Bifurcation Mech-anism in Switched Dynamical Systems

Dynamical model of a typical centrifugal flywheel governorsystem with periodic switches between two forms of exter-nal torque has been established. Two types of bifurcationcan be observed in the autonomous subsystem, where theHopf bifurcation may lead to the occurrence of periodicoscillation, while the fold bifurcation may result in the dis-appearance of the equilibrium points. The dynamics oftenbehaves in periodic oscillations with the same frequencyas the periodic switch. Generalized Hopf bifurcation maylead to the alternation of the behaviors between periodicmovements and quasi-periodic oscillations.

Yu V. WangYork College, The City University of New [email protected]

CP20

Gpu-Based Computational Studies of the Interac-tion Between Reentry Waves and Gap JunctionalUncoupling in Cardiac Tissues

The obstruction of coronary flow can cause cardiac arrhyth-mias including ventricular tachycardia and ventricular fib-rillation. Gap junctional uncoupling associates with thisprocess but to date the detailed underlying mechanism re-mains unclear. Our project investigates the dynamic re-lationship between gap junctional uncoupling and cardiacarrhythmia using GPU computing. This study promises todeepen our understanding of this phenomenon and couldenable us to control cardiac arrhythmia by manipulatingthe gap junctional coupling.

Zhihui ZhangFlorida State [email protected]

CP21

β1-Adrenergic Regulation of Action Potential andCalcium Dynamics in a Model of Mouse Ventricu-lar Myocytes

A detailed experimentally-based compartmentalized modelof the β1-adrenergic signaling system in mouse ventricu-lar myocytes is developed. Model simulations reproducedexperimental data on phosphorylation dynamics of majorionic currents and calcium binding proteins, voltage-clampdata on ionic currents, modulation of the cardiac mouse ac-tion potential and calcium transients by the β1-adrenergicsignaling system. Action mechanisms of phosphodiesteraseand protein kinase A inhibitors on the mouse action po-tential and calcium dynamics at the cellular level are dis-

DS15 Abstracts 109

cussed.

Vladimir E. BondarenkoDepartment of Mathematics and StatisticsGeorgia State [email protected]

CP21

A Mathematical Model for Frog PopulationDynamics with Batrachochydrium Dendrobatidis(Bd) Infection

Chytridiomycosis is a disease that poses a serious threat tofrog populations worldwide. Several studies confirmed thatinoculation of Janthinobacterium lividum (Jl) can inhibitthe disease. In this talk, I present a mathematical modelof a frog juvenile-adult population infected with chytrid-iomycosis caused by the fungal pathogen Batrachochydriumdendrobatidis (Bd) to investigate on how the inoculation ofanti-Bd bacterial species Jl could reduce Bd infection onfrogs.

Baoling MaUniversity of Louisiana - [email protected]

CP21

A Model of Heart Rate Dynamics for Changes inExercise Intensity

A nonlinear dynamical systems model for heart rate is in-vestigated for changes in exercise intensity. The modelequilibria are used to determine the instantaneous heartrate of an individual during acute bouts of exercise thatvary in intensity (power output) and cadence. Theoreticalpredictions show good agreement with laboratory cyclingtests that were performed on several healthy adults.

Michael J. MazzoleniDuke [email protected]

Claudio BattagliniUniversity of North Carolina at Chapel [email protected]

Brian MannDuke [email protected]

CP21

The Evolutionary Dynamics of Gamete Recogni-tion Genes

Fertilization of gametes in broadcast spawners such as seaurchins and abalone is modeled as a random walk processwith successful fertilization depending on variables such asbinding efficiency, sperm and egg concentration, and phys-ical characteristics of gametes. We develop a dynamicalsystem modeling the evolution of binding genes and illus-trate the conditions under which less efficient binding is fa-vored. The stability of different binding strategies exhibitsa complex series of bifurcations with increasing sperm con-centration.

David Mcavity, Mottet GenevaThe Evergreen State College


CP21

Spike Time Dependent Plasticity in a Spiking Neu-ral Network

To determine which inputs for a neuron are important andwhich information a neuron should listen to is an importantproblem during brain development and during learning.Spike-Timing Dependent Plasticity (STDP) is a physio-logical adaptation mechanism of synaptic regulation whichmake a neuron to determine which neighboring neuronsare worth by potentiating those inputs and depressing theother. We work on obtaining a good mathematical under-standing of Spike-Timing Dependent Plasticity (STDP).This involves understanding why STDP works so well andthe significance of factors like STDP type, learning windowand scaling under increasing network size. The mathemati-cal model we construct, by using phase oscillators is a goodexample of discrete adaptive asynchronous network. Thisis a joint work with Mike Field from Rice University.

Anushaya MohapatraOregon State [email protected]

Mike FieldRice University [email protected]

Chris BickRice [email protected]

CP22

Computational Topology Techniques for Charac-terizing Time Series Data

Full and accurate reconstruction of dynamics from time-series data—e.g., via delay-coordinate embedding—is areal challenge, but useful information can be gleaned fromincomplete embeddings. We apply computational topol-ogy to a sequence of lower-dimensional embeddings of thedata. Even though the full topology cannot be computedfrom these incomplete reconstructions, we conjecture thatthere are some results that can be computed from a se-quence of such reconstructions, and that these are usefulin time-series analysis.

Elizabeth BradleyUniversity of ColoradoDepartment of Computer [email protected]


Joshua T. GarlandUniversity of Colorado at BoulderDepartment of Applied [email protected]

Nicole SandersonUniversity of ColoradoDepartment of Mathematics

110 DS15 Abstracts

[email protected]

CP22

Plankton Models with Time Delay

We consider a three compartment (nutrient-phytoplankton-zooplankton) model with nutrient re-cycling. When there is no time delay the model has aconservation law and may be reduced to an equivalent twodimensional model. We consider how the conservation lawis affected by the presence of a state dependent time delayin the model. We study the stability and bifurcations ofequilibria when the total nutrient in the system is used asthe bifurcation parameter.

Sue Ann CampbellUniversity of WaterlooDept of Applied [email protected]

Matt KloostermanDept of Applied MathematicsUniversity of [email protected]

Francis PoulinDepartment of Applied MathematicsUniversity of [email protected]

CP22

Noise, Chaos and Entropy Generation in a Time-Delayed Dynamical System

Dynamical chaos and single photon detection are two phys-ical sources of randomness employed to generate fast, cryp-tographically secure random numbers. We present an ex-perimental system with both types of randomness: anelectro-optic feedback loop incorporating a single-photondetector. We describe how the dynamics change from shotnoise to deterministic chaos as the photon rate increases,and how the entropy rate can reflect either chaos or shotnoise depending on sampling rate and resolution.

Aaron M. Hagerstrom, Rajarshi RoyUniversity of [email protected], [email protected]

Thomas E. MurphyUniversity of Maryland, College ParkDept. of Electrical and Computer [email protected]

CP22

Stochastic Delay in Gene Regulation: Exact Sta-bility Analysis

Gene regulatory networks consist of interacting genes andproteins and they control the response of cells to envi-ronmental stimuli. The biochemical reactions involved ingene expression take finite time which lead to time delaysthat vary stochastically due to the inherent intracellularnoise. In this talk we analyze the dynamics of systemswith stochastic delays and derive exact stability conditionsof equilibria based on the second moment dynamics.

Mehdi Sadeghpour, Gabor OroszUniversity of Michigan, Ann Arbor

Department of Mechanical [email protected], [email protected]

CP23

Noise and Determinism of Stimulated BrillouinScattering Dynamics in Optical Fiber

Stimulated Brillouin scattering (SBS) is a noise-initiatednonlinear optical phenomenon that occurs in optical fiber.We present numerical modeling and experimental observa-tions of SBS in single-mode optical fiber. We employ sev-eral statistical methods to quantify and examine the rolesof determinism and stochasticity of SBS using time-delayembedding, false near neighbors and Hurst exponents. Ex-perimental and theoretical results display a transition inthe nature of statistical fluctuation properties from lowerto higher input powers.

Diana A. Arroyo-AlmanzaInstitute of Physical Science and Technology,University of [email protected]

Rafael Setra, Zetian NiUniversity of [email protected], [email protected]


Rajarshi RoyUniversity of [email protected]

CP23

Vector Rogue Waves and Dark-Bright BoomeronicSolitons in Autonomous and Non-Autonomous Set-tings

In this talk, I will discuss the dynamics of vector roguewaves and dark-bright solitons in two-component non-linear Schrodinger (NLS) equations with variable coeffi-cients. Using a suitable transformation for the wave func-tions, the two-component NLS system is converted into thewell-known integrable Manakov system. Then, the vectorrogue and dark-bright boomeron-like soliton solutions ofthe latter are converted back into ones of the original non-autonomous model. Using direct numerical simulations,I will present the formation and existence of such solitonsolutions in the non-autonomous case.

Efstathios CharalampidisDepartment of Mathematics and StatisticsUniversity of Massachusetts, [email protected]

R. BABU Mareeswaran, T. KannaPost Graduate and Research Department of PhysicsBishop Heber College, Indiababu [email protected], kanna [email protected]

Panayotis KevrekidisUniversity of [email protected]

Dimitri Frantzeskakis

DS15 Abstracts 111

University of [email protected]

CP23

Control of Extreme Events in the Bubbling On-set of Wave Turbulence in the Forced and DampedNon-Linear Schrodinger Equation

The existence of high amplitude intermittent fluctuationin many non-linear dynamical systems constitutes a prob-lem of great relevance in different fields of science. In thiswork we show the existence of an intermittent transitionfrom temporal chaos to turbulence in a spatially extendeddynamical system, namely the forced and damped one-dimensional non-linear Schrodinger equation. For somevalues of the forcing parameter the system dynamics in-termittently switches between ordered states and turbu-lent states, which may be seen as extreme events in somecontexts. In a Fourier phase-space the intermittency takesplace due to the loss of transversal stability of unstableperiodic orbits embedded in a low-dimensional chaotic at-tractor. We mapped these transversely unstable regionsand locally perturbed the system in order to significantlyreduce the occurrence of extreme events of turbulence.

Paulo GaluzioDepartment of PhysicsFederal University of [email protected]

Ricardo L. VianaDepartmento de FisicaFederal University of [email protected]

Sergio R. LopesDepartment of PhysicsFederal University of [email protected]

CP23

Reducibility of One-dimensional Quasi-periodicSchrodinger Equations

Consider the time-dependent linear Schrodinger equation

iqn = ε(qn+1+qn−1)+V (x+nω)qn+δ∑m∈Z

amn(θ+ξt)qm, n ∈ Z,

where V is a nonconstant real-analytic function on T , ωsatisfies a certain Diophantine condition and amn(θ) is

real-analytic on T b, b ∈ Z+, decaying with |m| and |n|.We prove that, if ε and δ are sufficiently small, then fora.e. x ∈ T and “most” frequency vectors ξ ∈ T b, it canbe reduced to an autonomous equation. Moreover, for thisnon-autonomous system, “dynamical localization” is main-tained in a quasi-periodic time-dependent way.

Jiansheng GengNanjing [email protected]

CP23

Numerical Continuation of Invariant Solutions ofthe Complex Ginzburg-Landau Equation

We compute solutions of the complex Ginzburg-Landauequation (CGLE) invariant under the action of the 3-dimensional Lie group of symmetries A(x, t) → eiθA(x +

σ, t+τ ). From an initial set of such solutions we obtain a se-quence of new sets of invariant solutions via numerical con-tinuation along paths in the parameter space of the CGLE.Solutions are obtained by solving an underdetermined sys-tem of nonlinear algebraic equations resulting from use ofa spectral-Galerkin discretization in both space and timeof the CGLE and the use of a path following method. Theset of initial solutions led to distinct, new invariant solu-tions of the CGLE in the final parameter region. All thesolutions are unstable, and have multiple modes and fre-quencies active, respectively, in their spatial and temporalspectra. Symmetry gaining/breaking behavior associatedwith the spatial reflection symmetry A(x, t) → A(−x, t)was common in the parameter regions traversed.

Vanessa LopezIBM Watson Research [email protected]

CP23

Nonlinear Oscillations and Bifurcations in SiliconPhotonic Resonators

Silicon microdisk resonators are micron-scale optical de-vices in which optical, thermal, electron/hole, and mechan-ical effects interact to produce a wide range of dynamicalphenomena. In the strongly nonlinear regime, we demon-strate the presence of Hopf and homoclinic bifurcationsleading to the onset and destruction of self-sustained os-cillations. We further show that the six-dimensional sys-tem of equations governing microdisk behavior can be re-duced to a nearly-one-dimensional relaxation-oscillator sys-tem, and qualitative dynamics are well represented by a toymodel.

Alexander Slawik, Daniel AbramsNorthwestern [email protected],[email protected]

CP24

Finding the Stokes Wave: From Low Steepness toAlmost Limiting Wave

A Stokes wave is a fully nonlinear wave that travels overthe surface of deep water. We solve Euler equations withfree surface in the framework of conformal variables viaNewton Conjugate Gradient method and find Stokes wavesin regimes dominated by nonlinearity. By investigatingStokes waves with increasing steepness we observe peculiaroscillations occur as we approach Stokes limiting wave. Fi-nally by analysing Pade approximation of Stokes waves weinfer that analytic structure associated with those waveshas branch cut nature.

Sergey DyachenkoUniversity of [email protected]

CP24

Blow-Ups in Nonlinear Pdes, Composite Grid-Particle Methods, and Stochastic Particle Systems

I will discuss a numerical method best suited for solvingevolution PDEs exhibiting singular and multiscale behavior(shocks or blow-ups). This method employs representationof solution simultaneously as a field (discretized on a gridor via finite elements) and a particle system. The fieldand the particles exchange mass according to criteria based

112 DS15 Abstracts

on the types of singularities that are formed in a givensystem. Examples with Keller-Segel equations of bacterialchemotaxis, Fisher-Kolmogorov, Burgers, and a few otherequations will be presented.

Ibrahim FatkullinUniversity of ArizonaDepartment of [email protected]

CP24

Singularities of the Stokes’ Wave: Numerical Sim-ulation

Two-dimensional potential flow of the ideal incompressiblefluid with free surface and infinite depth can be describedby a conformal map of the fluid domain into the complexlower half-plane. Stokes wave is the fully nonlinear gravitywave propagating with constant velocity.

Alexander O. KorotkevichDept. of Mathematics & Statistics, University of NewMexicoL.D. Landau Institute for Theoretical Physics [email protected]

CP24

Branch Cut Singularity of Stokes Wave

Stokes wave is the fully nonlinear gravity wave propagatingwith the constant velocity. We consider Stokes wave inthe conformal variables which maps the domain occupiedby fluid into the lower complex half-plane. Then Stokeswave can be described through the position and the typeof complex singularities in the upper complex half-plane.

Pavel M. LushnikovDepartment of Mathematics and StatisticsUniversity of New [email protected]

CP24

Coupled Parametrically Forced Oscillators andModulated Cross-Waves

Recent experiments and theory for subharmonic cross-waves in horizontally vibrated containers found slowlymodulated (quasiperiodic) solutions that cycle betweenbalanced and one-sided excitation. We analyze a gener-alized model of coupled parametrically forced oscillatorswith arbitrary relative phase to understand how these so-lutions arise, depending on coupling and forcing, and re-late this to an exchange symmetry permitted by specificforcing phases. A complex bifurcation scenario involvingsecondary modes and homoclinic bifurcations emerges inmany cases.

Jeff Porter, Pablo Salgado Sanchez, Ignacio Tinao, AnaLaveron-SimavillaUniversidad Politecnica de [email protected], [email protected],[email protected], [email protected]

CP25

Jetting-BubblingTransition in Microflows

Gas-liquid flows in microchannels are found to be primarilyof two types - jetting and bubbling. The dynamics of gas-

liquid micro flows is captured using viscous potential flow(VPF) theory. A linear stability analysis is carried outand the jetting to bubbling transition is predicted usingthe Briggs criterion of absolute-convective instability tran-sition. We study the effect of the wide parameter space(Reynolds number, Weber number, density ratio, viscosityratio and confinement) on this transition.

Dipin S. PillaiPh.D. ScholarIndian Institute of Technology Madras, [email protected]

S. PushpavanamProfessorIndian Institute of Technology Madras, [email protected]

CP25

Finding Model Parameters Without Prior Knowl-edge of Solve-Able Regions: A Solar Thermochem-istry Case-Study

Reduction of cobalt oxide nanoparticles is the first step ina solar thermochemical process to sustainably produce hy-drogen from water with concentrated sunlight. Using non-isothermal reaction data from the process as a case-study,we demonstrate a two-stage particle-swarm optimizationmethod to find kinetic parameters in the shrinking coremodel without a valid initial guess or bounding under mul-tiple, simultaneous rate-limiting conditions. The techniquedeveloped is broadly applicable to identifying parametersin data-fitting numerically intractable models.

Karl SchmittUniversity of Maryland, College ParkDept. of Mathematics, [email protected]

Luke VenstromValparaiso UniversityDept. of Mechanical [email protected]

William D. ArloffValparaiso [email protected]

Leandro JaimeValparaiso UniversityDept. of Mechanical [email protected]

CP25

Experiments on a Pinball-Like Oscillator

The response of a harmonically-excited mechanical systemin which a severe nonlinearity occurs due to an impact ispresented. The system receives a discrete input of energyat the impact condition: it is kicked. This is reminiscent ofthe unpredictability of the classic pinball machine. Closecorrelation is obtained between a mechanical experimentand numerical simulation, including unusual bifurcation se-quences and co-existing responses.

Lawrie N. VirginDepartment of Civil and Environmental EngineeringDuke University

DS15 Abstracts 113

[email protected]

CP25

Exploring the Hyperbolicity of Chaotic Rayleigh-Benard Convection

Covariant Lyapunov vectors allows us to quantify the di-rection of the stable and unstable manifolds of the tan-gent space for the high-dimensional chaotic dynamics ofRayleigh-Benard convection. The principal angle betweenthese manifolds can be used to determine the hyperbolicityof the dynamics. We use numerical simulations to computethe covariant Lyapunov vectors of Rayleigh-Benard convec-tion to probe fundamental features of the dynamics of anexperimentally accessible and high-dimensional system.

Mu Xu, Mark PaulDepartment of Mechanical EngineeringVirginia [email protected], [email protected]

CP25

Snakes on An Invariant Plane: CoupledTranslational-Rotational Dynamics of FlyingSnakes

Flying snakes of the genus Chrysopelea use body flatteningand three-dimensional body undulations in a dynamic yetcontrolled glide through air. Given this complexity, salientbody dynamics relevant to glide stability are unknown.We investigate a tandem airfoil model with snake-like fea-tures to better understand aerodynamic effects of undu-lation and translational-rotational mechanical coupling onmotion and stability during a glide. We elucidate somedynamical phenomena that occur including bifurcations,limit cycles, and a gliding manifold.

Isaac Yeaton, Hodjat Pendar, Jake SochaVirginia [email protected], [email protected], [email protected]


CP26

Constant Rebalanced Portfolio Strategy Is Ratio-nal in a Multi-Group Asset Trading Model

We evaluate the performance of various trading strategieswithin the context of the multi-group asset flow differentialequations model. We consider scenarios in which strate-gies vary continuously and slowly, and derive mathemat-ical justification for constant rebalanced portfolio (CRP)strategies. The CRP strategy minimizes investment risksas investor wealth is maintained when the price moves fromand then returns to its original value; non-CRP strategiesmay be exploited by others resulting in a loss of wealth.

Mark DeSantisMathematicsUniv of [email protected]

David SwigonDepartment of MathematicsUniversity of Pittsburgh

[email protected]

CP26

How Monetary Policy Can Cause Forecasting Un-certainty

Federal Reserve Chairwoman Yellen seems to be guidedby a rule that keeps interest rates low (high), when theeconomy is operating below (above) its trend. Instead ofstabilizing the economy, the unintended consequence of theYellen Rule is greater uncertainty, due to nonlinear feed-back. The resulting forecast errors can be modeled byapplying a Sprott nonlinear dynamical system of simplechaos, perturbed by random noise and shocked by excessdemand for real money.

James M. HaleyPoint Park [email protected]

CP26

Non-Smooth Dynamics and Bifurcations in aModel of Electricity Market

This paper proposes a model for the supply and demand ofelectricity in a domestic market based on system dynam-ics. Additionally, the model shows piecewise-smooth dif-ferential equations. Mathematical analysis and simulationexplain some counter-intuitive dynamics which also weredetected in practice. Then, a general model is proposed,which is closer to real electricity markets. Discontinuitieshave a large effect on the qualitative analysis. A first resultto be noted is the use of asynchronous maps for understand-ing what happens when parameters are varied, leading tonon-smooth bifurcations. To our knowledge. there are stillno reports in the literature about its use in socio-economicmarket systems. The other noteworthy result in this re-search is the effect that the ROI (Investment returns) hason the system dynamics since it leads to different surfaceswhose slope change according to the parameters.

Gerard Olivar TostDepartment of Mathematics and StatisticsUniversidad Nacional de Colombia - [email protected]

Johnny Valencia CalvoPh.D Candidate in Systems Engineering and ComputerSciencesSchool of Mines - Universidad Nacional de [email protected]

CP27

Towards Understanding Mechanisms of PainTransmission: a Systems Theoretic Approach

Pain is a universal experience. Motivated by a lack ofunderstanding of pain mechanisms, we develop a reducedlow-dimensional model of the dorsal horn circuit—the firstcentral relay of sensory inputs to the brain. We deter-mine how a cellular switch of firing patterns in dorsal horntransmission cells—tonic, plateau, endogenous bursting—contributes to a functional switch of information transfer—faithful transmission, enhancement, or blocking of nocicep-tive information.

Pierre SacreUniversity of Liege

114 DS15 Abstracts

[email protected]

Sridevi SarmaJohns Hopkins [email protected]

CP27

Optogenetic Stimulation of a Meso-Scale HumanCortical Model

Mesoscale models of cortical activity provide a means tostudy neural dynamics at the level of neuron populations,and offer a safe and economical way to test the effects andefficacy of stimulation techniques on the dynamics of thecortex. Here, we use a physiologically relevant mesoscalemodel of the cortex, consisting of a set of stochastic,highly non-linear partial differential equations, to studythe hypersynchronous activity of neuron populations dur-ing epileptic seizures. We use optogenetic stimulation tocontrol seizures in a hyperexcited cortex, and to induceseizures in a normally functioning cortex. The high spa-tial and temporal resolution this method offers makes astrong case for the use of optogenetics in treating epilep-tic seizures. We use bifurcation analysis to investigate theeffect of optogenetic stimulation in the meso scale model,and its efficacy in suppressing the non-linear dynamics ofseizures.

Prashanth SelvarajUniversity of California, [email protected]

Andrew J. SzeriUniversity of California at BerkeleyDepartment of Mechanical [email protected]

James W. SleighUniversity of AucklandWaikato Clinical [email protected]

Heidi E. KirschUC San [email protected]

CP27

Assessing the Strength of Directed InfluencesAmong Neural Signals

Inferring Granger-causal interactions between processespromises deeper insights into mechanisms underlying net-work phenomena, e.g. in the neurosciences where the levelof connectivity in neural networks is of particular interest.Renormalized partial directed coherence can be used to in-vestigate Granger causality in such multivariate systems.A major challenge in estimating respective coherences is areliable parameter estimation of vector autoregressive pro-cesses. We discuss improvements of the estimation pro-cedure that are particularly relevant in the neurosciences.

Linda SommerladeFreiburg Center for Data Analysis and ModelingUniversity of [email protected]

Marco Thiel


Claude WischikTauRx Therapeutics [email protected]

Bjoern SchelterInstitute for Complex Systems and Mathematical [email protected]

CP27

Analysis of Cholera Epidemics with BacterialGrowth and Spatial Movement

In this work, we propose novel epidemic models for choleradynamics by incorporating a general formulation of bacte-ria growth and spatial variation. In the first part, a general-ized ODE model is presented and it is found that bacterialgrowth contributes to the increase of the basic reproductionnumber. With the derived basic reproduction number, weanalyze the local and global dynamics of the model. Par-ticularly, we give a rigorous proof on the endemic globalstability by employing the geometric approach. In the sec-ond part, we extend the ODE model to a PDE model withthe inclusion of diffusion to capture the movement of hu-man hosts and bacteria in a heterogeneous environment.The disease threshold of this PDE model is studied againby using the basic reproduction number. The results onthe threshold dynamics of the ODE and PDE models arecompared, and verified through numerical simulation.

Xueying WangWashington State [email protected]

CP27

Benefits of Noise in Synaptic Vesicle Release

Noise is not only a source of disturbance but can also bebeneficial for neuronal information processing. The releaseof neurotransmitter vesicles in synapses is an unreliableprocess, especially in the central nervous system. Here westudy the effect of the probabilistic nature of this processand show that how stochasticity in vesicle docking and re-lease can be beneficial for synaptic transmission.

Calvin Zhang, Charles S. PeskinCourant Institute of Mathematical SciencesNew York [email protected], [email protected]

CP27

Growth Dynamics for Pomacea Maculata

Pomacea maculata is a relatively new invasive species to theGulf Coast region and potentially threatens local agricul-ture (rice) and ecosystems (aquatic vegetation). The pop-ulation dynamics of Pomacea maculata have largely beenun-quantified. We directly measured the growth rates of in-dividually marked snails grown in a common tank to quan-tify their growth patterns. However, due to large intra- andinter- individual variability and sample size, we were notable to get statistically rigorous estimates (i.e., tight confi-dence intervals) on overall growth dynamics. However, wewere able to use a model comparison statistic to determinethat there are distinct growth stages. Further, these data

DS15 Abstracts 115

strongly suggest that male and female growth dynamics,size distributions, and overall weights, are notably differentwith females being generally larger. We performed simu-lation studies based on observed variability, and are usingthese models to design additional lab experiments and fieldstudies.

Lihong ZhaoUniversity of Louisiana at Lafayette, [email protected]

Karyn L. SuttonUniversity of [email protected]

Jacoby CarterUSGS National Wetlands Research [email protected]

CP28

Optimal Control of Building’s Hvac System withon-Site Energy Storage and Generation System

Commercial and residential buildings consume more than40% of the total energy in most countries, and HVAC(Heating Ventilation and Air Conditioning) systems typ-ically consume more than 50% of the building energy con-sumption. A recent study indicates that optimal controlof HVAC system can achieve energy savings of up to 45%.Therefore, optimized control of HVAC system can poten-tially reduce significant amount of energy consumption ofbuildings. In this work, we describe a model predicted con-trol (MPC) framework that optimally computes the controlprofiles of the HVAC system considering the dynamic de-mand response signal, on-site storage of electricity, on-sitegeneration of electricity, greenhouse gas emission as well asoccupants comfort. The approach would determine how topower the HVAC system from the optimal combination ofgrid electricity, on-site stored electricity and on-site gener-ated electricity.

Raya HoreshIBM T.J. Watson Research [email protected]

Young M. LeeIBM T.J. Watson Reseach [email protected]

Leo LibertiIBMLIX, Ecole Polytechnique, Palaiseau, [email protected]

Young Tae ChaeHyundai Engineering & Construction Co., LtdResearch and Development Division , Seoul, Republic [email protected]

Rui ZhangIBM T.J. Watson Reseach [email protected]

CP28

Optimal Treatment Strategies for HIV-TB Co-

Infected Individuals

Initiating anti-HIV treatment during ongoing TB treat-ment for HIV-TB co-infected individuals has advantagesand disadvantages. Here, we develop a dynamical system(system of ODEs) that helps identify an ideal treatmentstrategy for HIV-TB co-infected individuals. Using ourmodel, we formulate and analyze an optimal control prob-lem in order to determine a HIV-TB treatment protocolthat provides a minimum cumulative burden from this co-infection.

Abhishek MallelaUniversity of Missouri-Kansas [email protected]

Suzanne M. LenhartUniversity of TennesseeDepartment of [email protected]

Naveen K. VaidyaDept of Maths & Stats, University of Missouri - KansasCityKansas City, Missouri, [email protected]

CP28

Towards a Structural Theory of Controllability ofBinary Networks

Almost all complex networks satisfy structural controlla-bility theory except for some special networks which forma set of Lesbesgue measure zero. A important class of net-works is binary networks, that is networks for which all ofthe existing connections have the same associated weight.However, these networks often do not satisfy structuralcontrollability theory. We focus on this class of networksand propose some graphical tools that can be used to char-acterize the structural controllability of binary networks.

Afroza ShirinGraduate StedentsDepartment of Mechanical Engineering, University ofNew [email protected]

CP29

Stripe to Spot Transition in a Plant Root Hair Ini-tiation Model

A generalised Schnakenberg system with source and lossterms and a spatially dependent coefficient of the nonlin-ear term is studied in 2D. The system captures active andinactive forms of the kinetics of a small G-protein ROP,which are catalysed by a gradient of the plant hormoneauxin. Localised stripe-like solutions of active ROP oc-cur for high enough total auxin concentration and lie on acomplex bifurcation diagram of single and multi-pulse so-lutions. Transverse stability computations show that these1D solutions typically undergo a transverse instability intospots. The spots so formed typically drift and undergosecondary instabilities such as spot replication. A 2D nu-merical continuation analysis is performed that shows thevarious stable hybrid spot-like states can coexist. Upondescribing the dispersion relation of a certain non-localeigenvalue problem, the parameter values studied lead to

116 DS15 Abstracts

an analytical explanation of the initial instability.

Victor F. Brena-MedinaUniversity of [email protected]

Daniele AvitabileSchool of Mathematical SciencesUniversity of [email protected]

Alan R. ChampneysUniversity of [email protected]

Michael WardDepartment of MathematicsUniversity of British [email protected]

CP29

Symmetry Groups and Dynamics of Time-Fractional Diffusion Equation

In science and engineering the processes in which both spa-tial and temporal variations occur are often known as dif-fusion. Mostly diffusion process is anomalous due to theheterogeneous nature of medium therefore it can be bestdescribed in terms of fractional derivatives. We proposea new approach to construct the symmetry groups of frac-tional diffusion equation and using these groups we providesome interesting physical interpretation to understand thedynamics of anomalous diffusion.

Muhammad D. KhanInstitute of Business [email protected]

CP29

Onset of Singularities in the Pattern of Fluctua-tional Paths of a Nonequilibrium System

A generic feature of systems away from thermal equilib-rium is the occurrence of singularities in the patterns ofmost probable trajectories followed in rare fluctuations toremote states in phase space. We study how the singu-larities emerge as the system is driven away from thermalequilibrium by an increasingly strong perturbation. Wefind where there is a threshold in the perturbation strengthand the scaling of the singularity location if there is nothreshold.

Oleg B. KoganCornell [email protected]

Mark I. DykmanDepartment of Physics and AstronomyMichigan State [email protected]

CP29

Polynomial Mixing Rates of Particle Systems

In this talk I will present our results on polynomial mixingrates of some particle systems that are derived from thestudy of microscopic heat conduction. We rigorously provethat an energy dependent Kac-type model admits polyno-

mial mixing rates ∼ t−2. In the end, I will show that sim-ilar slow (polynomial) mixing rates appear in many othermicroscopic heat conduction models.

Yao LiCourant Institute of Mathematical Sciences,New York [email protected]

MS1

Nonlinearity Saturation as a Singular Perturbationof the Nonlinear Schrodinger Equation

Saturation of a Kerr-type nonlinearity in the generalizednonlinear Schrodinger equation (NLS) can be regarded asa singular perturbation which regularizes the well knownblow-up phenomenon in the cubic NLS. An asymptotic ex-pansion is proposed which takes into account multiple scalebehavior both in the longitudinal and transverse directions.We find that interaction of a solitary wave and an adja-cent wave field is governed by behavior of eigenfunctionsof the linearized fast-scale operator. In one dimension, thesolitary wave acts solely to reflect impinging waves andaccelerates by an elastic transfer of momentum. In twodimensions, the solitary wave can be made transparent tothe ambient field for a certian value of wave power. Thisis joint work with Jordan Allen-Flowers.

Karl GlasnerThe University of ArizonaDepartment of [email protected]

MS1

Dark-Bright, Dark-Dark, Vortex-Bright and OtherMulti-Component NLS Beasts: Theory and RecentApplications

Motivated by recent work in nonlinear optics, as well asin Bose-Einstein condensate mixtures, we will explore aseries of nonlinear states that arise in such systems. Wewill start from a single dark-bright solitary wave, and thenexpand our considerations to multiple such waves, theirspectral properties, nonlinear interactions and experimen-tal observations. A twist will be to consider the darksolitons as effective potentials that will trap the brightones, an approach that will also prove useful in charac-terizing the bifurcations and instabilities of the system.Beating, so-called dark-dark soliton variants of such stateswill be touched upon. Generalizations of all these notionsin higher dimensions and, so-called, vortex-bright solitonswill also be offered.


MS1

Bifurcation and Competitive Evolution of NetworkMorphologies in the Strong Functionalized Cahn-Hilliard Equation

The Functionalized Cahn Hilliard (FCH) is a higher-orderfree energy for blends of amphiphillic polymers and solventwhich balances solvation energy of ionic groups againstelastic energy of the underlying polymer backbone. Itsgradient flows describe the formation of solvent networkstructures which are essential to ionic conduction in poly-mer membranes. The FCH possesses stable, coexisting

DS15 Abstracts 117

network morphologies and we characterize their geometricevolution, bifurcation and competition through a center-stable manifold reduction which encompasses a broad classof coexisting network morphologies. The stability of thedifferent networks is characterized by the meandering andpearling modes associated to the linearized system. Forthe H−1 gradient flow of the FCH energy, using func-tional analysis and asymptotic methods, we drive a sharp-interface geometric motion which couples the flow of co-dimension 1 and 2 network morphologies, through the far-field chemical potential. In particular, we derive expres-sions for the pearling and meander eigenvalues for a classof far-from-self-intersection co-dimension 1 and 2 networks,and show that the linearization is uniformly elliptic off ofthe associated center stable space.

Noa KraitzmanMichigan State [email protected]

MS1

Nonlinear Stability of Source Defects

Defects are interfaces that mediate between two wavetrains. Of particular interest in applications are sourcesfor which the group velocities of the wave trains to eitherside of the defect point away from the interface. Whilesources are ubiquitous in experiments, their stability anal-ysis presents many challenges. In this talk, I will discussnonlinear-stability results for sources that rely on pointwiseestimates.

Bjorn SandstedeDivision of Applied MathematicsBrown Universitybjorn [email protected]

MS2

Dynamics of Autonomous Boolean Networks

Autonomous Boolean networks are known to display com-plex dynamics, originating from the absence of an externalclock, internal time delays and the non-ideal behaviour ofthe logic gates. We study experimentally such networks ona field-programmable gate array (FPGA). In particular,we show that networks consisting of only a few logic ele-ments can produce long transients. We demonstrate howthese transients can be used to successfully perform reser-voir computing, a new machine learning paradigm.

Otti D’Huys, Nicholas D. HaynesDepartment of Physics, Duke [email protected], [email protected]

Miguel C. SorianoIFISC (UIB-CSIC)Campus Universitat de les Illes Balears, Palma [email protected]

Ingo FischerCampus Universitat de les Illes BalearsIFISC (UIB-CSIC)[email protected]

Daniel J. GauthierDepartment of Physics, Duke University

[email protected]

MS2

Gene Network Models Including mRNA and Pro-tein Dynamics

Qualitative models of gene regulatory networks have gener-ally considered transcription factors to regulate directly theexpression of other transcription factors, without any inter-mediate variables. In fact, gene expression always involvestranscription, which produces mRNA molecules, followedby translation, which produces protein molecules, whichcan then act as transcription factors for other genes. Sup-pressing these multiple steps implicitly assumes that thequalitative behaviour does not depend on them. Here weexplore a class of expanded models that explicitly includesboth transcription and translation, keeping track of bothmRNA and protein concentrations. We mainly deal withregulation functions that are steep sigmoids or step func-tions, as is often done in protein-only models. Our resultsthus show that including mRNA as a variable may changethe behavior of solutions.

Roderick EdwardsUniversity of [email protected]

MS2

Database for Switching Networks As a Tool forStudy of Gene Networks

Continuous time Boolean networks, or switching networks,represent an attractive platform for qualitative studies ofgene regulation, since the dynamics at fixed parameters isrelatively easily to compute. However, it is quite difficultto analytically understand how changes of parameters af-fect dynamics. Database for Dynamics is an excellent toolfor studying these models, as it rigorously approximatesglobal dynamics over a parameter space. The results ob-tained by this method provably capture the dynamics apredetermined spatial scale. We combine these two ap-proaches to present a method to study switching networksover a parameter spaces. We apply our method to experi-mental data for cell cycle dynamics.

Tomas GedeonMontana State UniversityDept of Mathematical [email protected]

MS2

Evolution of Gene Networks

Genetic activity is partially regulated by a complicatednetwork of proteins called transcription factors. An out-standing scientific puzzle is to understand how this geneticnetwork can evolve. I discuss evolution of dynamics in sim-plified models of genetic networks. By changing the logicalstructure randomly, it is possible to evolve the networks inan effort to identify networks that display rare dynamics -e.g. networks with long stable cycles or with a high levelof topological entropy. In the context of the models, it ispossible to estimate optimal mutation rates. The theoreti-cal models pose the problem of how evolution can robustlytake place in organisms.

Leon GlassMcGill University

118 DS15 Abstracts

Department of [email protected]

MS3

Controlling Long-Term Spatial Distributions ofAutonomous Vehicles in Stochastic Flow Environ-ments

We present a control strategy for aquatic vessels that lever-ages the environmental dynamics and noise to efficientlynavigate in a stochastic fluidic environment using the the-ory of large fluctuations. We show that a vehicle’s like-lihood of transition between regions in the flow can bemanipulated by the proposed control strategy, resulting inefficient navigation from one region to another. We thenexperimentally verify the strategy in a fluid environmentusing autonomous vehicles.

Christoffer R. HeckmanU.S. Naval Research [email protected]

Ani HsiehDrexel [email protected]


MS3

Tracking of Geophysical Flows by Robot Teams:An Experimental Approach

This talk presents our group’s recent efforts in using teamsof robots to track geophysical fluid features like LagrangianCoherent Structures. The talk will focus on our develop-ment of the multi-robot Coherent Structure Testbed anovel multi-robot experimental testbed capable of creatingocean-life flows in a laboratory setting. I will show ex-perimental results of various single vehicle and multi-robotcontrol strategies for tracking different fluidic features in aflow field and navigating in stochastic flows.

Ani Hsieh, Dhanushka Kularatne, Dennis LarkinDrexel [email protected], [email protected],[email protected]

Eric ForgostonMontclair State UniversityDepartment of Mathematical [email protected]

Philip YeckoCooper [email protected]

MS3

Conditional Statistics with Lagrangian CoherentStructures

Coherent structures are ubiquitous in the environment. Inorder to analyze mixing and transport processes, condi-tional statistics are typically generated and scaling laws areidentified. Classically, these are based on flow domain par-titions from Eulerian quantities. However, recent studies

show that Eulerian quantities are not invariant subject toarbitrary frame translation and rotation. We show in thistalk scalar dispersion and residence time statistics basedon Lagrangian partitions, where new scaling law behaviorsare identified.

Wenbo Tang, Phillip WalkerArizona State [email protected], [email protected]

MS3

Controlled Lagrangian Prediction Using An En-semble of Flow Models

The technique of controlled Lagrangian prediction (CLP)is developed to employ an ensemble of flow modes to pro-vide odometry-like localization information for underwatervehicles. CLP can then be fused with other underwaterlocalization technology to enable simultaneous localizationand map-making (SLAM). Map-making functionality willbe performed to update each flow model with the latestsensor information and to decide the best flow model touse that gives the minimum localization error at any giventime.

Fumin ZhangSchool of Electrical and Computer EngineeringGeorgia Institute of [email protected]

MS4

Constrained Motion of Point Vortices InteractingDynamically with Rigid Bodies in Ideal Flow

The equations of motion for the dynamic interaction ofrigid bodies and point vortices in ideal flow were only re-cently derived, in 2002 by Shashikanth et al and in 2003by Borisov et al. We compare these equations with thoseobtained by a suitable application of Diracs method of con-straints to the N-vortex problem. In 2008, Vankerschaveret al derived the unconstrained equations through symplec-tic reduction, but several assumptions were made in theanalysis. We investigate the possibility of relaxing some ofthese assumptions.

Michael Fairchild, Scott KellyUNC [email protected], [email protected]

MS4

The Poincare-Hopf Theorem in Nonholonomic Me-chanics

This talk discusses using the Poincare-Hopf theorem andthe technique of Hamiltonization as a means to studythe integrability nonholonomic mechanical systems (briefly,mechanical systems subject to non-integrable velocity con-straints). We will focus primarily on a generalized Klebsh-Tisserand case of the Suslov problem, and use the afore-mentioned approach to determine the topology of the (two-dimensional) invariant manifolds, and in particular theirgenus. The results will be contrasted with those expectedof Hamiltonian systems.

Oscar FernandezWellesley [email protected]

Anthony M. Bloch

DS15 Abstracts 119

University of MichiganDepartment of [email protected]

Dmitry ZenkovNorth Carolina State UniversityDepartment of [email protected]

MS4

Discretization of Hamiltonian Incompressible Flu-ids

The geometry of incompressible, inviscid fluids can bedescribed by Arnold’s classic formulation in terms ofgeodesics on the Lie group of volume-preserving diffeo-morphisms. In recent years this formulation has been dis-cretized for computational purposes, creating a geomet-ricnumerical method that obeys a discretized version ofKelvin’s circulation theorem. This talk will present an ex-tension of this discretization into the corresponding Hamil-tonian view of incompressible inviscid fluids, thereby givinga method based on the vorticity equation. Along the waywe will discuss the general principles of this style of dis-cretization, which involves approximating the Lie group ofvolume-preserving diffeomorphisms by a finite-dimensionalLie-group and then localizing the resulting equations bymeans of a non-holonomic constraint.

Gemma MasonCMS [email protected]

Christian LessigTechnishe Universitat [email protected]

Mathieu DesbrunDept. of Computing & Mathematical [email protected]

MS4

The Lie-Dirac Reduction for Nonholonomic Sys-tems on Semidirect Products

We consider Dirac systems with symmetry for nonholo-nomic mechanical systems on Lie groups with broken sym-metry. We show reduction of Lagrange-Dirac systems andDirac-Hamilton systems in the context of Lie-Dirac re-duction with advected parameters. Then, we develop im-plicit Euler-Poincare-Suslov and Lie-Poisson-Suslov equa-tions with advected parameters with some illustrative ex-amples such as the Chaplygins ball and the second orderRivlin-Ericksen fluids. We also discuss the Dirac reductionon semidirect products by stages on the Hamiltonian side.

Hiroaki YoshimuraWaseday [email protected]

Francois Gay-BalmazEcole Normale Superieure de Paris

[email protected]

MS5

Combined Effects of Connectivity and Inhibition ina Model of Breathing Rhythmogenesis

The pre-Btzinger complex is an area in the brainstem whichgenerates the breathing rhythm, an essential function forlife. We model this area with realistic bursting neuronscoupled in a large sparse network. We study how syn-chronous activity of the population changes due to (1) thenumber of connections each cell receives (2) the fraction ofcells which are inhibitory, and (3) the strength of excitatoryand inhibitory synapses. The model is compared to exper-imental data. We also ask, how do multiple phases of ac-tivity arise? Can they arise spontaneously in unstructurednetworks, or do they require more structured networks likeblock models?

Kameron D. HarrisApplied MathematicsUniversity of [email protected]

Tatiana DashevskiyCenter for Integrative Brain ResearchSeattle Children’s Research [email protected]

Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected]

Jan-Marino RamirezCenter for Integrative Brain ResearchUniversity of [email protected]

MS5

A Complex Networks Approach to Malaria’s Ge-netic Recombination Dynamics

Malaria parasites evade immune systems by sequentiallyexpressing diverse proteins on the surface of infected redblood cells. These camouflage proteins come from rapidgenetic recombination that shuffles the genes that encodethe proteins. Because this shuffling precludes the use oftraditional sequence analysis techniques, we take a newapproach by mapping sequences to a network in whicheach vertex represents a single sequence and constraintson recombination reveal themselves in the networks com-munity structure. We validate this approach on syntheticsequences. Application of this technique to a large set of se-quences from both human- and ape-infecting malaria para-sites reveals that the observed genetic states of six distinctmalaria species have arisen due to recombining and evolv-ing a common set of initial sequence content, dating backprior to the speciation of humans and chimpanzees fromtheir most recent common ancestors.

Daniel B. Larremore, Caroline BuckeeCenter for Communicable Disease DynamicsHarvard School of Public [email protected], [email protected]

Aaron ClausetUniversity of Colorado at Boulder

120 DS15 Abstracts

Computer [email protected]

MS5

Not-So-Random Graphs Through Wide Motifs

This work focuses on two powerful analytical methodsthat can model stochastic processes on (and/or of) com-plex networks: one recasts the problem as a set of ordi-nary differential equations, and the other amounts to abranching process. Both methods are based on the idea ofbreaking the network into smaller pieces—hereafter called”motifs”—that may be re-assembled according to specificrules. However, these techniques are limited to randomgraphs containing no cycles, except for the cycles explic-itly represented within the motifs used in their assembly.This is a major problem for real-world phenomenons (suchas cascading failures due to flows reorganization) that fun-damentally depend on the presence of cycles much longerthan what these motifs-based methods allow. In this work,I will present recent developments concerning ”wide mo-tifs”, which generalize both the concepts of ”motifs” and”tree decomposition”. By opposition to traditional motifs,cycles may be broken into pieces to span multiple widemotifs, thus allowing for cycles of arbitrarily long lengthsthat may share intricate overlaps. This perspective can beused for a broad spectrum of networks, spanning from de-terministic structures to random graphs, thus blurring theline between these extremes. The approach broadens theclass of problems that can be approached analytically andintroduces new challenges in the detection and characteri-zation of network structures. Conceptual similarities with”belief propagation” algorithms and the ”tensor network”representation of entangled quantum states should allowfor these different fields to cross-fertilize.

Pierre-Andre NoelDepartment of Mechanical EngineeringUniversity of California, [email protected]

MS5

Causal Network Inference by Optimal CausationEntropy

The abundance of time series data, which is in sharp con-trast to limited knowledge of the underlying network dy-namic processes that produce such observations, calls fora general and efficient method of causal network infer-ence. We develop mathematical theory of Causation En-tropy (CSE), a model-free information-theoretic statisticdesigned for causality inference. We prove that for a givennode in the network, the collection of its direct causalneighbors forms the minimal set of nodes maximizing Cau-sation Entropy, a result we refer to as the Optimal Causa-tion Entropy (oCSE) Principle, for which we develop ef-ficient algorithms. Analytical and numerical results forGaussian processes on large random networks highlightthat inference by oCSE outperforms previous leading meth-ods including Conditional Granger Causality and TransferEntropy. Interestingly, our numerical results also indicatethat the number of samples required for accurate inferencedepends strongly on network characteristics such as thedensity of links and information diffusion rate and not onthe number of nodes.

Jie Sun, Erik BolltClarkson [email protected], [email protected]

Dane TaylorStatistical and Applied Mathematical Sciences InstituteDept of Mathematics, University of North Carolina,Chapel [email protected]

MS6

Model-Based Glucose Forecasting for Type 2 Dia-betics

Type 2 diabetes affects 9 million Americans. While treat-ment is complex, two important components include quan-tifying the features of glucose dynamics and forecastingthe effect of nutrition on glucose levels. Both topics areaddressed in this talk. First, electronic health record dataare used to identify features of glucose dynamics that cor-relate with mortality via a regression. Second, a dual un-scented Kalman filter and two mechanistic models are usedto forecast glucose using real data.

David J. AlbersColombia UniversityBiomedical [email protected].

MS6

Predicting Recovery of Consciousness in Patientswith Brain Injury

Oscillatory electrical activity is associated with informa-tion processing in the brain. Patients with severe braininjuries often exhibit disorders of consciousness along withdisturbed oscillatory activity. This project was designedto determine whether continuous measures of brain oscil-lations can be used to predict recovery of consciousness onthe time-scale of days. Sparse partial least squares andhigh-dimensional classification algorithms are used to de-termine latent variables used for prediction in a novel sub-set of patients.

Hans-Peter FreyDepartment of Neurology, Columbia [email protected]

MS6

Assimilating Sleep - Putting the Model to the Data

Over the past four years we investigated tools for data as-similation and forecasting from models of the sleep-wakeregulatory system. Ill report on the challenges we now faceas we collect data from brainstem cell groups in freely be-having animals and attempting to apply these tools.

Bruce J. GluckmanPenn State [email protected]

MS6

Time Series Modeling and Analysis Using Elec-tronic Health Record Data

Electronic health record data contain valuable informationabout biology and health care, but the data hold a num-ber of challenges, including the fact that measurementsare sparse and irregular. Furthermore, health care is ahighly complex process that makes drawing causal conclu-sions very difficult. We discuss alternate time parameteri-zations that may lead to a more stationary time series, and

DS15 Abstracts 121

we discuss the use of Granger causality to tease out causesand confounders.

George HripcsakDepartment of Bioinfomatics, Columbia [email protected]

MS7

Reconstruction of Structural Connectivity in Neu-ronal Networks Using Compressive Sensing of Net-work Dynamics

Taking into account the prominence of sparsity in neuronalconnectivity, we develop a framework for efficiently re-constructing neuronal connections in a sparsely-connected,feed-forward network model with nonlinear dynamics.Driving the network with a small ensemble of random stim-uli, we derive a set of underdetermined linear systems relat-ing the network connectivity to neuronal firing rates. Viacompressive sensing, we accurately recover sparse networkconnectivity and also realistic network inputs distinct fromthe training set of stimuli.

Victor BarrancaNew York [email protected]

Douglas ZhouShanghai Jiao Tong [email protected]

David CaiCourant Institute for Mathematical Sciences, NYUShanghai Jiao-Tong [email protected]

MS7

Theoretical Modeling of Neuronal Dendritic Inte-gration

We address the question of how a neuron integrates excita-tory (E) and inhibitory (I) inputs from different dendriticsites. For an idealized neuron with an unbranched den-drite, a conductance-based cable model is derived and itsasymptotic solutions are constructed. The solutions revealthe underlying mechanisms of a dendritic integration rulediscovered in a recent experiment. We then extend ouranalysis to the multi-branch case and confirm our analysisthrough numerical simulation of a realistic neuron.

Songting Li, Douglas ZhouShanghai Jiao Tong [email protected], [email protected]

David CaiNew York UniversityCourant [email protected]

MS7

Functional Connectomics from Data: ConstructingProbabilistic Graphical Models for Neuronal Net-works

The nervous system of the nematode Caenorhabditis el-egans (C. elegans) is comprised of 302 neurons for whichelectro-physical connectivity map (i.e. connectome) is fullyresolved. Although the static connectome is available, in-

ference of dominant neural pathways that control sensori-motor responses is challenging since neurons are dynamicalobjects and interactions within the network are also dy-namic. In our study, we construct a Probabilistic GraphicalModel (PGM) for the C. elegans connectome that repre-sents the ’effective connectivity’ between the neurons (cor-relations) and takes into account the dynamics. The struc-ture of the PGM is learned using Bayesian methods capableof learning the structure of an undirected graphical modelfrom a collection of time series. The collections are ob-tained by a systematic excitation of neurons in a recentlydeveloped computational dynamical model for the C. ele-gans that simulates single neural responses and interactionsbetween the neurons (synaptic and gap). Bayesian infer-ence methods applied to the constructed PGM allow us toextract neural pathways in the connectome of C. elegans re-sponsible for experimentally well characterized movementsof the worm such as forward and backward locomotion. Inaddition, we show that the framework allows for inferenceof pathways that correspond to movements that were notfully characterized in experiments and to perform ’reverse-engineering’ studies in which a typical setup on the mo-tor neurons layer is imposed and dominant pathways thatpropagate to the sensory layer through the interneuronslayer are being identified.

Eli ShlizemanUniversity of [email protected]

MS7

Topology Reconstruction of Neuronal Networks

Current experimental techniques usually cannot probe theglobal interconnection pattern of a network. Thus, recon-structing or reverseengineering the network topology ofcoupled nodes based upon observed data has become a veryactive research area. Most existing reconstruction methodsare based on networks of oscillators with generally smoothdynamics. However, for nonlinear and non-smooth stochas-tic dynamical systems, e.g., neuronal networks, the recon-struction of the full topology remains a challenge. Here, wepresent a noninterventional reconstruction method, whichis based on Granger causality theory, for the widely usedconductance-based, integrate-and-fire type neuronal net-works. For this nonlinear system, we have established adirect theoretical connection between Granger causal con-nectivity and structural connectivity.

Douglas ZhouShanghai Jiao Tong [email protected]

Yanyang Xiao, Yaoyu Zhang, Zhiqin XuDepartment of Mathematics and Institute of NaturalSciencesShanghai Jiao Tong [email protected], [email protected],[email protected]


MS8

Investigation of Boussinesq non-linear Interactions

122 DS15 Abstracts

Using Intermediate Models

Nonlinear coupling among wave modes and vortical modesis dissected in order to probe the question: Can we dis-tinguish the wave-vortical interactions largely responsiblefor formation versus evolution of coherent, balanced struc-tures? It is well known that the quasi-geostrophic (QG)equations can be derived from the Boussinesq system ina non-perturbative way by ignoring wave interactions andconsidering vortical modes only. One qualitative differencebetween those two models is the lack of skewness in theQG dynamics. In this talk, non-perturbative intermediatemodels that include more and more classes of non-linearinteractions will be used to identify their role in differentqualitative properties of the Boussinesq system. Numericalresults will be shown to describe the effect of each class inthe transfer of energy between vortical modes and waves,transfer of energy (or the lack of it) between scales, forma-tion of vortices and skewness.

Gerardo Hernandez-DuenasNational University of Mexico, JuriquillaInstitute of [email protected]

Leslie SmithMathematics and Engineering PhysicsUniversity of Wisconsin, [email protected]

Samuel StechmannUniversity of Wisconsin - [email protected]

MS8

Internal Wave Generation by Convection

When a convectively unstable region is adjacent to a stablystratified region, the convection can produce internal waveswithin the stable region. This is thought to occur in stars,gaseous planets, the Earths atmosphere, oceans and lakes,and possibly even the Earths core. We describe a modelfor estimating the wave generation by convection based onLighthills theory, and compare the model to high-resolutionsimulations using the Dedalus code.

Daniel LecoanetUC BerkeleyAstronomy [email protected]

Keaton BurnsMIT Kavli Institute for Astrophysics and Space [email protected]

Geoffrey M. VasilTheoretical Astrophysics CenterAstronomy Department, University of California,[email protected]

Eliot [email protected]

Benjamin BrownLASP and Dept. Astrophysical & Planetary SciencesUniversity of Colorado, [email protected]

Jeffrey OishiDepartment of PhysicsFarmingdale State [email protected]

MS8

Interaction of Inertial Oscillations with aGeostrophic Flow

The interaction between large horizontal scale pure iner-tial oscillations and small horizontal scale geostrophic fieldis investigated in this work. As a result of the interac-tion rapid vertically propagating near inertial waves andtrapped or non-propagating inertial oscillations form. Thetrapped oscillations inherit smaller spatial scales from thegeostrophic field and remains in the upper ocean. The nearinertial waves propagate into the deep ocean within days,thus allowing the inertial signal to be felt in the deep ocean.The study hence offers an alternate explanation for the ageold problem of vertical propagation of near inertial wavesand formation of small scale inertial oscillations in an ide-alized set up. The interaction is however non-energetic,which is consistent with previous works.

Jim ThomasNew York UniversityCourant [email protected]

Shafer SmithCenter for Atmosphere Ocean ScienceCourant [email protected]

Oliver BuhlerCourant Institute of Mathematical SciencesNew York [email protected]

MS8

Interactions Between Near-Inertial Waves and Tur-bulence in the Ocean

Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial(or Coriolis) frequency. The corresponding near-inertialwaves (NIWs) are highly energetic and play a significantrole in the slow, large-scale dynamics of the ocean. Toanalyse this role, we develop a new model of the nondissi-pative interactions between NIWs and mean flow using avariational implementation of the generalised-Lagrangian-mean formalism. The new model couples the Young & BenJelloul model of NIWs with a quasi-geostrophic model inwhich the relation between potential vorticity and stream-function is modified by a quadratic wave term. The modelreveals that NIWs act as an energy sink for the mean flow:NIWs forced at large scales experience a horizontal scalecascade through refraction and advection; as a result, theirpotential energy increases at the expense of the mean en-ergy. The implications for ocean energetics are discussed.

Jacques VannesteSchool of MathematicsUniversity of Edinburgh

DS15 Abstracts 123

[email protected]

MS9

Local Inference of Gene Regulatory Networks fromTime Series Data

Temporal dynamics of gene expression levels may be par-tially explained by interactions between certain proteins,called transcription factors, which act to either promoteor repress RNA-synthesis (transcription) of specific genes.Discovering the regulatory relationships in these transcrip-tion networks is a difficult goal of systems biology, butone which promises to greatly enhance experimental de-sign. In this talk, we describe a statistical approach toinfer the structure of gene regulatory networks from timeseries data.

Francis C. Motta, Kevin McGoff, Anastasia Deckard, XinGuo Guo, Tina Kelliher, Adam Leman, Steve Haase,John HarerDuke [email protected], [email protected],[email protected], [email protected],[email protected], [email protected],[email protected], [email protected]

MS9

Patterns in Discrete Ecological Dynamical SystemsRevealed Through Persistent Homology

Persistent homology captures information about a systemregarding longevity of topological features, such as levelsets of a function. This provides a novel perspective whenapplied to discrete time dynamical systems. In particu-lar, interesting patterns arise when applied to the logisticmap; a common population model. This pattern will bediscussed and extended to other systems, including contin-uous systems.

Rachel NevilleColorado State [email protected]

MS9

Network Spread and Control of Invasive Speciesand Infectious Diseases

We introduce a method for coupling vector-based trans-portation networks (e.g. agents traveling by vehicle) onto aspatially continuous model of a biological epidemic. Anal-ysis for plant invasions yields a unique, stable, steady-statesolution with an optimal control for the infected vectors,with network topology affecting the efficacy of the con-trol. Numerical results are shown for the cheatgras invasionof Rocky Mountain National Park based on the presencemodel of Strickland et al. 2014.

Christopher StricklandSAMSI Statistical and Mathematical Sciences [email protected]

Patrick ShipmanDepartment of MathematicsColorado State University

[email protected]

MS9

Topological Data Analysis for and with Contagionson Networks

The study of contagions on networks is central to the un-derstanding of collective social processes and epidemiol-ogy. When a network is constrained by an underlyingmanifold such as Earth’s surface (as in most social andtransportation networks), it is unclear how much spread-ing processes on the network reflect such underlying struc-ture, especially when long-range edges are also present. Weaddress the question of when contagions spread predomi-nantly via the spatial propagation of wavefronts (e.g., asobserved for the Black Death) rather than via the appear-ance of spatially-distant clusters of contagion (as observedfor modern epidemics). To provide a concrete scenario, westudy the Watts threshold model (WTM) of social conta-gions on what we call noisy geometric networks, which arespatially-embedded networks that consist of both short-range and long-range edges. Our approach involves us-ing multiple realizations of contagion dynamics to map thenetwork nodes as a point cloud, for which we analyze thegeometry, topology, and dimensionality. We apply suchmaps, which we call WTM maps, to both empirical andsynthetic noisy geometric networks. For the example of anoisy ring lattice, our approach yields excellent agreementwith a bifurcation analysis of the contagion dynamics. Im-portantly, we find for certain dynamical regimes that wecan identify the network’s underlying manifold in the pointcloud, highlighting the utility of our method as a tool forinferring low-dimensional (e.g., manifold) structure in net-works. Our work thereby finds a deep connection betweenthe fields of dynamical systems and nonlinear dimensionreduction.

Dane TaylorStatistical and Applied Mathematical Sciences InstituteDept of Mathematics, University of North Carolina,Chapel [email protected]

Florian KlimmMaster of Science (Physics)Humboldt-Universitat, [email protected]

Heather HarringtonUniversity of [email protected]

Miroslav KramarRutgers UniversityDepartment of [email protected]

Konstantin MischaikowDepartment of MathematicsRutgers, The State University of New [email protected]

Mason A. PorterUniversity of OxfordOxford Centre for Industrial and Applied [email protected]

Peter J. MuchaUniversity of North Carolina Chapel Hill

124 DS15 Abstracts

[email protected]

MS10

Stability Analysis of PDEs with Two Spatial Di-mensions Using Lyapunov Methods and SOS

In this talk we consider stability of parabolic linear partialdifferential equations with polynomial coefficients and twospatial variables. We use Sum-of-Squares, polynomial opti-mization, and the Positivstellensatz to numerically searchfor quadratic inhomogeneous Lyapunov functions. Nega-tivity of the derivative is enforced using a new type of slackvariable called a ”spacing function”. The technique wastested numerically on a two-dimensional biological PDEmodel of population growth model and compared to theanalytic solution.

Evgeny Meyer, Matthew PeetArizona State [email protected], [email protected]

MS10

Differential Equations with Variable Delay andTheir Connection to Partial Differential Equations

Time delay systems can be described by delay differentialequations or by a partial differential equation (PDE) withnon-local boundary conditions. The domain of the PDE isequal to the state space interval of the delay system. Forvariable delays a moving boundary appears in the PDErepresentation. Conditions for a transformation from vari-able delay (domain) to constant delay (domain) are stud-ied, leading to a fundamental dichotomy of variable delaysystems with qualitatively different properties.

Gunter RadonsChemnitz University of [email protected]

Andreas OttoInstitute of PhysicsChemnitz University of [email protected]

David MuellerChemnitz University of [email protected]

MS10

Delayed Boundary Conditions in Control of Con-tinua

The mechanical model of a basic problem of electroacous-tics is considered. The governing PDE is the 1D waveequation with delayed boundary conditions. The systemcan be transformed into a delay differential equation ofneutral type with two delays. The zero-measure regionsare constructed analytically in the parameter plane of thegain parameter and the ratio of the delays where the sys-tem is exponentially stable. The physical relevance of thispeculiar stability chart is highlighted.

Gabor StepanDepartment of Applied MechanicsBudapest University of Technology and [email protected]

Li Zhang

Nanjing University of Aeronautics and [email protected]

MS10

What Is Wrong with Non-Smooth Mechanics andHow Memory Effects Can Fix It?

Non-smooth mechanics has many intricacies. It can pro-vide some surprising predictions or even fail to predictthe dynamics past certain singularities. Such singularitieswhere the equations break down include various forms ofthe Painleve paradox and the two-fold singularity of fric-tional systems. This talk looks at the reasons why thesesingularities occur and addresses the issue by adding morephysics to the mechanical model. It turns out that finitewave-speed within the mechanical system is sufficient forunique predictions, which can be taken into account witha single correction term dependent only on the wave speedand geometry.

Robert SzalaiUniversity of [email protected]

MS11

Phase Transitions in Models for Social Dynamics

Flocking models abound in the recent mathematical andscientific literature. These models can be applied to or-ganisms which exhibit collective behavior; such models areoften applied to insects, fish, birds, and even to humans. Iwill introduce several flocking models, both deterministicand stochastic, at the microscopic scale. I will then discusstheir kinetic and hydrodynamic limits and show that phasetransitions can occur on all three scales.

Alethea BarbaroCase Western Reserve [email protected]

MS11

A Center Manifold and Complex Phases for a LargeNumber of Interacting Particles

We investigate a system of ordinary differential equations(ODEs) describing interacting particles, with applicationsto schools of fish. This model has many advantages overdiscrete systems of interacting particles and seems to cap-ture the interactions of animals better than the classicaldiscrete Czirok-Vicsek (or boids) model. The main differ-ence is that in our system the animal is allowed to adjust itsvelocity as well as direction to that of its neighbors. This isthe behavior observed in nature and it makes our systemmore suitable to applications to real animals. The sys-tem of ODEs can also be analyzed using methods from dy-namical systems and it turns out to have a two-parameter(velocity and direction) asymptotic solution as t becomeslarge. It also possesses a very rich set of stationary solu-tions that all are unstable.In this talk we discuss the center manifold of the migrat-ing state (attractor) and applications to simulations of an-chovies off the coast of Peru and Chile. The effects of ElNino will also discussed.

Bjorn BirnirUniversity of CaliforniaDepartment of [email protected]

DS15 Abstracts 125

Luis BonillaUniversidad Carlos III de MadridG. Millan Institute of Fluid Dynamics, Nanoscience &[email protected]

Jorge Cornejo-DonosoUCSBBren [email protected]

MS11

Modeling Earthquake Cycles on Faults SeparatingVariable Materials

We have developed a computational method for studyinghow the earthquake cycle is affected by heterogeneities inthe material surrounding a fault. Finite difference oper-ators satisfying a summation-by-parts rule are applied tothe 2D elastodynamic wave equation and weak enforce-ment of boundary conditions are enforced through thesimultaneous-approximation-method. This combined ap-proach leads to a provably stable and high-order accuratemethod. Non-planar fault geometries, variable materialsand inelastic response are incorporated. As a first step weconsider the bimaterial problem on planar, vertical strikeslip fault. We find that rupture propagates in the pre-ferred direction and we are currently studying the longterm behavior of the earthquake cycle and under what con-ditions rupture in the non-preferred direction (periodicallyobserved on natural faults) is possible.

Brittany EricksonPortland State [email protected]

MS11

Mathematical Challenges in Ground State Forma-tion of Isotropic and Anisotropic Interaction

In this talk we will present a mathematical framework forstudying ground state formation in a general class of kine-matic models which are often used to understand the phys-ical, biological and social world. I will first discuss the caseof when particles communicate isotropically and, time per-mitting, will present new developments in the mathemati-cal theory of anisotropic pattern formation.

David T. UminskyUniversity of San FranciscoDepartment of [email protected]

MS12

Synchronization over Networks Inspired by Echolo-cating Bats

While number of organisms have made use of active sen-sory systems, bats are particularly effective at echoloca-tion, wherein they emit ultrasonic waves and sense echoesto navigate their environment. One of the greatest chal-lenges of echolocating in a group is jamming, which oc-curs when echoes from an individuals calls become diffi-cult to distinguish from those of its peers. Nevertheless,bats are observed to avoid the negative effects of jammingin behavioral experiments. Drawing inspiration from thisphenomenon, we incorporate the effect of jamming into aclassical model of synchronization among coupled dynamic

systems by superposing a disturbance topology on the com-munication network. Within this framework, we developconditions for stochastic synchronization and the rate ofconvergence to synchronized states.

Subhradeep Roy, Nicole AbaidVirginia Polytechnic Institute and State [email protected], [email protected]

MS12

Versatile Vibrations: Partially Synchronized Statesin Mechanical Systems from Microns to Kilometers

In this talk I’ll describe the dynamics of coupled oscil-lators in three systems: optomechanical microdisk res-onators, mechanical metronomes, and pedestrians on sus-pension bridges. Though drastically different in origin andin scale, the equations of motion share many similarities. Iwill present analytical and numerical techniques for solvingthose equations and discuss some unsolved problems andopen questions regarding networks of coupled oscillators.

Daniel AbramsNorthwestern [email protected]

MS12

Wind-Induced Synchrony Causes the Instability ofa Bridge: When Millennium Meets Tacoma

We aim at better understanding the cause of dangerous vi-brations and bridges collapsing as a result of wind-inducedoscillations at a frequency different from the natural fre-quencies of a bridge, including the collapse of the TacomaNarrows Bridge and a long-wave resonance vibration ofthe Volga Bridge. We propose a synchronization-basedmechanism that can explain the shift of the resonant fre-quency due to wind-induced synchronization of suspensioncables/load-bearing elements of a bridge. We also drawparallels between wind-excitation and crowd synchronyand present a bifurcational, analytically tractable model,inspired by the Millennium Bridge case.

Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected]

Russell JeterGeorgia State [email protected]

Vladimir BelykhLobachevsky State University of Nizhny Novgorod, [email protected]

MS12

Network Graph Can Promote Faster ConsensusReach Despite Large Inter-Agent Delays

This presentation stems from the authors work on the inter-play between delays, graphs, and dynamical systems. Here,we consider a class of widely-studied linear consensus prob-lem with inter-agent communication delays. For this classof systems, it is known that consensus is guaranteed only ifthe inter-agent delay is less than a certain margin, knownas the delay margin. We investigate how delays and thearising graph formed by agent connectivity can influence

126 DS15 Abstracts

the speed of reach of agents to consensus. Since the solu-tion to this problem is analytically intractable, simulationstudies with randomization are systematically performedto investigate it. The three non-trivial findings are as fol-lows: (i) for large inter-agent delays less than the delaymargin, there exist some particular graphs that promoteconsiderably faster reach of agents to consensus, (ii) for agiven graph, consensus in the presence of larger delays canbe reached faster if inter-agent couplings are weaker butnot stronger, (iii) for small size networks, there seems tobe a way to decide which inter-agent links to remove inorder for the agents to reach consensus faster. These pre-liminary results call for further research in the pursuit ofrevealing the most immune graphs that also promote largedecay rate in system states of various dynamical systems,against the detrimental effects of delays.

Min Hyong KohNortheastern [email protected]

Rifat SipahiDepartment of Mechanical and Industrial EngineeringNortheastern [email protected]

MS13

Stochastic Boundary Conditions for Molecular Dy-namics: From Crystal to Melt

Motivated by the need for closure relations in continuum-atomistic simulations, we develop non-periodic moleculardynamic boundary conditions with consistent dynamics totraditional NPT algorithms. A hypothesized stochasticmodel is employed at the boundary and parameters arefit on the fly via statistical sampling of the interior. Sucha method allows us to examine non-traditional computa-tional domains that allow us to focus on interfaces whileaccounting for local curvatures.

Gregory J. HerschlagDepartment of MathematicsDuke [email protected]

Sorin MitranUniversity of North Carolina Chapel [email protected]

MS13

Tipping and Warning Signs for Patterns and Prop-agation Failure in SPDEs

In this talk, I shall report on recent results regarding early-warning signs for pattern formation in stochastic partialdifferential equations. In particular, it will be shown thatclassical scaling laws from stochastic ordinary differentialequations can be carried over to the SPDE case. Thisis illustrated in the context of the Swift-Hohenberg equa-tion, analytically and numerically. Furthermore, I shalldiscuss numerical results for warning signs for the stochas-tic Fisher-KPP equation in the case of noisy invasion fronttraveling waves near positive absorption probability eventsleading to propagation failure. Several interesting potentialfuture directions for dynamical systems analysis of SPDEswill also be sketched.

Christian KuehnVienna University of Technology

[email protected]

Karna V. GowdaNorthwestern [email protected]

MS13

Fluctuating Hydrodynamics of Microparticles inViscoelastic Fluids

Abstract not available.

Scott McKinleyUniversity of [email protected]

MS13

Low-Damping Transition Times in a FerromagneticModel System


Katherine NewhallCourant Institute of Mathematical ScienceNew York [email protected]

MS14

Topological Detection of Structure in Neural Ac-tivity Recordings

In biology, observations are often related to variables ofinterest through unknown monotonic nonlinearities. De-tecting structure in the presence of such nonlinearities canbe challenging, as eigenvalue-based methods are often mis-leading. However, algebro-topological tools can providemeasurements robust to such transformations, allowing thedetection of the presence or absence of intrinsic structure.To demonstrate, we detect the geometric structure arisingfrom hippocampal place cells directly from neural record-ings.

Chad GiustiWarren Center for Network and Data SciencesUniversity of [email protected]

Carina Curto, Vladimir ItskovPennsylvania State [email protected], [email protected]

MS14

An Algebro-Topological Perspective on Hierarchi-cal Modularity of Networks

(Joint work with R. Levi and S. Raynor) Recent researchby, among others, Bassett and her collaborators, has shownthat brain networks exhibit hierarchical modularity, whichvaries with time during learning. In this talk I will describework on applying methods from algebraic topology in anattempt to characterize and classify those hierarchicallymodular graphs that arise as brain networks.

Kathryn Hess

Ecole Polytechnique Federale De Lausanne

DS15 Abstracts 127

[email protected]

MS14

The Topology of Fragile X Syndrome

Fragile X syndrome (FXS) is the most common knowninherited cause of developmental disability and the mostcommon single-gene risk factor for autism. In this talk Iwill give a brief description of the algorithm used by Map-per/Iris to produce a Reeb-like graph representation from adataset, and then describe how its application to MRI datahas led to the potential identification of higher and lowerfunctioning subgroups within a population of children withFXS.

David RomanoStanford School of [email protected]

MS14

The Neural Ring: Using Algebraic Geometry toAnalyze Neural Codes

Neurons represent external stimuli via neural codes, andthe brain infers properties of a stimulus space using onlythe intrinsic structure of the neural code. We define theneural ring, an algebraic object that encodes the combina-torial data of a neural code. Neural rings can be expressedin a ‘canonical form’ that translates to a minimal descrip-tion of code’s structure. This provides information aboutstructure in the stimulus space, and how changing the codeaffects these properties.

Nora YoungsDepartment of MathematicsHarvey Mudd [email protected]

MS15

Modeling Excitable Dynamics of Cardiac Cells

In the past decades many mathematical models of differ-ent complexity have been devised describing the excitabledynamics of cardiomyocytes and cardiac tissue. To assessthese models their ability to predict experimental cardiacdynamics has to be probed. The model evaluation canbe performed in a data assimilation frame work where themodel is driven by measured data and after some tran-sient time the input is switched off and the output of thefree running model is compared to the true evolution ofthe experimental system. To assess the fidelity of selectedmodels we employ different state and parameter estimationalgorithms, and apply them to experimental data.

Sebastian BergMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected]

T.K. Shajahan, Jan Schumann-BischoffMax Planck Institute for Dynamics and [email protected], [email protected]

Ulrich Parlitz, Stefan LutherMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical Physics


MS15

Reconstructing Dynamics of Unmodeled Variables

Assimilation of data with models of physical processes isa crucial component of modern scientific analysis. In re-cent years, nonlinear versions of Kalman filtering have beendeveloped, in addition to methods that estimate model pa-rameters in parallel with the system state. We propose asubstantial extension of these tools to deal with the specificcase of unmodeled variables, when training data from thevariable is available. The method uses a stack of several,nonidentical copies of a physical model to jointly recon-struct the variable in question. We demonstrate the abilityof this technique to accurately recover an unmodeled ex-perimental quantity, such as an ion concentration, from asingle voltage trace after the training period is completed.The method is applied to reconstruct the potassium con-centration in a neural culture from multielectrode arrayvoltage measurements.

Franz HamiltonGeorge Mason [email protected]

Timothy SauerDepartment of Mathematical SciencesGeorge Mason [email protected]

MS15

Intramural Forecasting of Cardiac Dynamics UsingData Assimilation

As a first step in reconstructing the three-dimensionalpropagation and breakup of electrical waves, a data-assimilation system is coupled to a simple model of car-diac electrical dynamics. Data assimilation is a techniquecommon in numerical weather prediction for combining ob-servations with a numerical model to derive an improvedestimate of the state of a dynamical system. Here an en-semble Kalman filter is used on synthetic data for both 1Dand 3D models.

Matthew J. HoffmanRochester Institute of [email protected]

Elizabeth M. CherryRochester Institute of TechnologySchool of Mathematical [email protected]

MS15

Tracking Neuronal Dynamics During Seizures andAlzheimer’s Disease

Observability of a dynamical system requires an under-standing of its statethe collective values of its variables.However, existing techniques are too limited to measureall but a small fraction of the physical variables and pa-rameters of neuronal networks. We constructed models ofthe biophysical properties of neuronal membrane, synaptic,and microenvironment dynamics, and incorporated theminto a model-based framework from modern control the-ory. We demonstrated the meaningful estimation of thedynamics of small neuronal networks using as few as a sin-

128 DS15 Abstracts

gle measured variable. Specifically, we assimilated noisymembrane potential measurements from individual hip-pocampal neurons to reconstruct the dynamics of networksof these cells, their extracellular microenvironment, andthe activities of different neuronal types during seizures.We used reconstruction to account for unmeasured partsof the neuronal system, relating micro-domain metabolicprocesses to cellular excitability, and validate the recon-struction of cellular dynamical interactions against actualmeasurements. Recently, we applied the method to intra-cellular Ca2+ dynamics using cytoplasmic Ca2+ as an ob-servable to reconstruct and identify the differences betweenmitochondrial bioenergetics in control and Alzheimers dis-ease states.

Ghanim UllahUniversity of South [email protected]

MS16

Feasibility of Micro-Grid Adoptions in Spatially-Embedded Urban Networks

We present a data-driven citywide simulation scheme thatcombines heterogeneous demand with a complex systemsapproach. We present micro grid simulations via DC powerflow dynamics combined with real (photovoltaic) PV gener-ation and demand profiles of individual buildings in a city,modeled after high temporal-resolution smart-grid data.We explore the efficiency of spatial networks at three dif-ferent scales from individual buildings to micro-grid neigh-borhoods to an entire city.

Marta GonzalezCivil and Environmental [email protected]

MS16

Cascading Failures and Stochastic Methods forMitigation in Spatially-Embedded Random Net-works

We have demonstrated that cascading failures are non-self-averaging in spatial graphs, hence predictability is poorand conventional mitigation strategies are largely ineffec-tive. In particular, we have shown that protecting all nodes(or edges) by the same additional capacity (tolerance) canactually lead to larger global failures, i.e., ”paying more canresult in less”, in terms of robustness. Here, we explorestochastic methods for optimal distribution of resources(capacities) subject to a fixed total cost.

Gyorgy KornissDepartment of Physics, [email protected]

MS16

Spatial Distribution of Population and Scaling inHuman Travel

An interesting scaling law connecting the travel time anddistance was recently observed in human traveling modesand information spreading. Further we go, faster we dothat. Seemingly the spatial distribution of population andthe presence of hubs are responsible for this very generalphenomenon. Investigating the connection between pop-ulation density distribution and the mean traveling speed

brings new clues to understand this puzzling phenomenonand optimize human travel and information flow.

Zoltan NedaBabes-Bolyai UniversityDepartment of [email protected]

Geza TothHungarian Central Statistical [email protected]

Andras KovacsEdutus CollegeDepartment of International [email protected]

Istvan Papp, Levente VargaBabes-Bolyai UniversityDepartment of [email protected], [email protected]

MS16

The Brain in Space

Based on experimental evidence here we argue that com-puting in the brain is based on deeply physical principlesin which form follows function: although there is a com-plex network of computing elements, this network is notan abstract graph, but a physical network embedded bothin space and time and these physical properties are justas much part of information processing in the brain as thesignals themselves that are being transmitted through thenetwork.

Zoltan ToroczkaiUniversity of [email protected]

Maria Ercsey-RavaszFaculty of PhysicsBabes-Bolyai University, [email protected]

Kenneth Knoblauch, Henry KennedyStem cell and Brain Research Institute, INSERM U846Bron, [email protected], [email protected]

MS17

On the Role of Stochastic Delays in Gene Regula-tory Networks

In gene regulatory networks delays emerge from sequen-tial assembly and accumulation of macromolecules. Fur-thermore, the stochastic nature of biochemical processesleads to stochastic variations in the delay. This may leadto counter intuitive dynamics where increasing uncertaintycan increase the robustness of the system. In this talk wepresent novel methods that allow us to evaluate the exactstability of equilibria in systems with stochastic delays. Wedemonstrate these tools on an auto-regulatory network.

Marcella Gomez, Matthew BennettRice [email protected], [email protected]

Richard Murray

DS15 Abstracts 129

Control and Dynamical SystemsCalifornia Institute of [email protected]

MS17

New Mechanisms for Patterns, Transitions, andCoherence Resonance for Systems with DelayedFeedback

Controlling patterns via delayed feedback is an efficientmeans of pattern resilience. Computations demonstratecomplex dynamics for PDE’s with Pyragas control. Wegive a new analysis for stochastic PDE’s with delay, cap-turing novel spatio-temporal pattern mechanisms in theSwift-Hohenberg equation (SHE) with Pyragas control, notobserved for the standard SHE. We show that travelingwaves appear via coherence resonance-type phenomena andcompare these to other multimode patterns generated bydelays.

Rachel KuskeUniversity of British [email protected]

Chia LeeUBC [email protected]

Vivi RottschaeferMathematical InstituteLeiden [email protected]

MS17

Dynamics with Stochastically Delayed Feedback:Designing Connected Vehicle Systems

In this talk we present novel mathematical tools that allowone to evaluate the dynamics of systems where stochactic-ity appears in the feedback delay. In particular we analyzethe mean and second moment dynamics in order to evalu-ate absolute and convective instabilities in networked sys-tem. We apply these methods to networks of vehicles thatexchange information via vehicle-to-vehicle (V2V) commu-nication. In such systems stochastic delays appear due tointermittencies and packet loss.

Gabor Orosz, Wubing QinUniversity of Michigan, Ann ArborDepartment of Mechanical [email protected], [email protected]

MS17

Synchronization of Degrade-and-Fire OscillationsVia a Common Activator

In this talk, we examine an experimentally motivatedstochastic model for coupled degrade-and-fire gene oscil-lators, where a core delayed negative feedback establishesoscillations within each cell, and a shared delayed positivefeedback couples all cells. We use analytic and numeri-cal techniques to investigate conditions for one cluster andmulti-cluster synchrony. A nonzero delay in the sharedpositive feedback, as expected for experimental systems, isfound to be important for synchrony to occur.

William H. MatherVirginia Tech Physics

[email protected]

Jeff HastyDepartment of BioengineeringUniversity of California, San [email protected]

Lev S. TsimringUniversity of California, San [email protected]

MS18

Homoclinic Snaking Near a Codimension-twoTuring-Hopf Bifurcation Point

Spatiotemporal Turing-Hopf pinning solutions near a codi-mension two Turing-Hopf point are studied. Both theTuring and Hopf bifurcations are supercritical and sta-ble. The pinning solutions exhibit coexistence of stationarystripes of near critical wavelength and time periodic oscilla-tions near the characteristic Hopf frequency. The solutionbranches are organized in a series of saddle-node bifurca-tions similar to snaking structures of stationary pinning so-lutions. Time dependent depinning dynamics outside thesaddle-nodes are illustrated. Wavelength variation withinthe snaking region is discussed, and reasons for the varia-tion are given in the context of amplitude equations. Thepinning region is compared favorably to the Maxwell linefound numerically by time evolving the amplitude equa-tions

Justin C. TzouDalhousie [email protected]

Yiping MaDepartment of Applied MathematicsUniversity of Colorado, [email protected]

Alvin BaylissNorthwestern [email protected]

Bernard J MatkowskyDepartment of Engineering Sciences and AppliedMathematicsNorthwestern [email protected]

Vladimir A. VolpertNorthwestern [email protected]

MS18

Localised Solutions in a Non-Conservative Cell Po-larization Model

We study a reaction-diffusion model for cell polarization,which exhibits pinned front solutions as a consequence ofmass conservation. When a source and a sink term areadded to the model, the front solutions vanish. This givesrise to spike solutions and the snaking scenario. Usingnumerical and analytical tools, we characterize these be-haviours. Finally we investigate the connection betweenthe snaking and front solutions, when the non-conservative

130 DS15 Abstracts

terms tend to zero.

Nicolas Verschueren Van Rees, Alan ChampneysUniversity of [email protected], [email protected]

MS18

Slow Dynamics of Localized Spot Patterns forReaction-Diffusion Systems on the Sphere

In the singularly perturbed limit corresponding to largea diffusivity ratio between two components in a reaction-diffusion (RD) system, many such systems admit quasi-equilibrium spot patterns, where the solution concentratesat a discrete set of points in the domain. In this context, wederive and study the differential algebraic equation (DAE)that characterizes the slow dynamics for such spot patternsfor the Brusselator model on the surface of a sphere. Local-ized spot patterns can undergo a fast time instability andwe derive the conditions for this phenomena, which dependon the spatial configuration of the spots and the parame-ters in the system. In the absence of these instabilities,our numerical solutions of the DAE system for N = 2 toN = 8 spots suggest a large basin of attraction to a smallset of possible steady-state configurations. We discuss theconnections between our results and the study of point vor-tices on the sphere, as well as the problem of determininga set of elliptic Fekete points, which correspond to globallyminimizing the discrete logarithmic energy for N points onthe sphere.

Philippe H. TrinhProgram in Applied and Computational MathematicsPrinceton [email protected]

Michael WardDepartment of MathematicsUniversity of British [email protected]

MS18

The Origin of Finite Pulse Trains: HomoclinicSnaking in Excitable Media

Many physical, chemical and biological systems exhibittraveling waves as a result of either an oscillatory insta-bility or excitability. The latter may admit a large mul-tiplicity of stable and spatially localized wavetrains con-sisting of different numbers of traveling pulses. The ex-istence of these states is related here to the presence ofhomoclinic snaking in the vicinity of a subcritical, finitewavenumber Hopf bifurcation. The pulses are organizedin a slanted snaking structure resulting from the presenceof a heteroclinic cycle between small and large amplitudetraveling waves. Connections of this type require a multi-valued dispersion relation. This dispersion relation is com-puted numerically and used to interpret the profile of thepulse group. The different spatially localized pulse trainscan be accessed by appropriately customised initial stimulithereby blurring the traditional distinction between oscil-latory and excitable systems.

Arik YochelisJacob Blaustein Institutes for Desert Research, SedeBoqerBen-Gurion University of the [email protected]


MS19

A Geometric Approach to Stationary Defect Solu-tions

In this talk we consider the impact of a very simple andsmall spatial heterogeneity on the existence of localizedpatterns in a system of PDEs in one spatial dimension.The existence problem reduces to the problem of finding aheteroclinic orbit in an ODE in ‘time’ x, for which the vec-tor field for x ¿ 0 differs slightly from that for x ¡ 0, underthe assumption that there is such an orbit in the unper-turbed problem. We show that both the dimension of theproblem as well as the nature of the linearized system nearthe endpoints of the heteroclinic orbit has a remarkablyrich impact on the existence these defect solutions.

Arjen DoelmanMathematisch [email protected]


Feng XieMathematisch Instituut, Leiden UniversityDept. of Appl. Math., Donghua [email protected]

MS19

Reformulating Spectral Problems with the KreinMatrix

Successful resolution of spectral problems in Hamiltoniansystems require that we locate not only the eigenvalues,but we also determine the Krein signature of those whichare purely imaginary. The well-known Evans function de-termines the location and multiplicity of the eigenvalues,but in its classical form it does not allow a determinationof the signature. On the other hand, the Krein matrix,and the accompanying Krein eigenvalues, allow us to notonly find the eigenvalues, but the graphs can be used todetermine the signature. We will briefly consider the con-struction of the matrix, and discuss its role in applications.

Todd KapitulaCalvin CollegeDept of Math & [email protected]

MS19

Stability in Spatially Localized Patterns

Motivated by numerical stability results on spatially local-ized patterns in spatially extended systems, we show howthe stability of patterns that are formed of nonlocalizedfronts can be understood from the spectra of the underly-ing fronts. We use extended Evans functions to understandthe spectral properties of these patterns on the original un-bounded domain and on large but bounded domains andcompare our results to previous findings on resonance poles

DS15 Abstracts 131

and edge bifurcations.

Elizabeth J. MakridesBrown UniversityDivision of Applied Mathematicselizabeth [email protected]


MS19

Existence of Pearled Patterns in the Planar Func-tionalized Cahn-Hilliard Equation

The functionalized Cahn-Hilliard (FCH) equation supportsplanar and circular bilayer interfaces as equilibria whichmay lose their stability through the pearling bifurcation: aperiodic, high-frequency, in-plane modulation of the bilayerthickness. In two spatial dimensions we employ spatial dy-namics, a center manifold reduction, normal form analy-sis and a fixed-point-theorem argument to show that thereduced system admits a degenerate 1:1 resonant normalform, from which we deduce that the onset of the pearlingbifurcation coincides with the creation of a two-parameterfamily of pearled equilibria which are periodic in the in-plane direction and exponentially localized in the trans-verse direction.

Qiliang WuMichigan State [email protected]

MS20

Homeostasis As a Network Invariant

The simplest mathematical definition of homeostasis is asfollows. Suppose a system X = F (X) has a stable equilib-rium X0 and the system depends on an input parameterI . Homeostasis occurs when one of the variables of X0(I)— say the jth — is approximately constant over a broadrange of I . We translate finding homeostasis to finding sin-

gular points∂X0

j

∂I(I0) = 0. We discuss the question: When

are homeostasis singularities invariants of the system whenviewed as a network?

Martin GolubitskyOhio State UniversityMathematical Biosciences [email protected]

Ian StewartUniversity of [email protected]

MS20

Optimized Networks Have Cusp-like Dependenceon Structural Parameters

Using synchronization stability as a prototypical exam-ple, we demonstrate a general phenomenon observed incomplex networks of coupled dynamical units: the opti-mization of collective dynamics leads to cusp-like depen-dence on network-structural parameters, such as the num-ber of nodes/links and the magnitude of structural per-turbations. We show that this phenomenon is observed

in a wide range of systems, including Turing instability inactivator-inhibitor systems and the dynamics of generatorsin power grids.

Takashi Nishikawa, Adilson E. MotterNorthwestern [email protected], [email protected]

MS20

Symmetries, Cluster Synchronization, and IsolatedDesynchronization in Complex Networks

Many networks are observed to produce patterns of syn-chronized clusters, but their prediction in general is dif-ficult. We use computational group theory to find net-work symmetry and cluster synchronization. The numberof symmetries can be astronomically large. We show thisexperimentally using an electro-optic network. We observea surprising phenomenon (isolated desynchronization) inwhich some clusters lose synchrony while leaving othersconnected to them synchronized. This is explained by asubgroup decomposition of the group.

Louis M. PecoraNaval Research [email protected]

Francesco SorrentinoUniversity of New MexicoDepartment of Mechanical [email protected]

Aaron M. HagerstromUniversity of [email protected]

Rajarshi RoyUniversity of Maryland, College Park, MD, [email protected]


MS20

Symmetry Breaking and Synchronization Patternsin Networks of Coupled Oscillators

In a recent paper [1] we considered the dynamics of a col-lection of oscillators coupled to form a network and weshowed that the analysis of the network symmetries canbe used to predict the emergence of cluster synchroniza-tion patterns. In particular, we focused on a specific solu-tion corresponding to the partition of the network nodes inclusters, characterized by the ‘maximal symmetry’. In gen-eral, given a network, there are other cluster synchronoussolutions that may emerge, which correspond to symmetrybreakings of the maximal symmetry solution. While in [1],we presented a method to characterize this one solutionand its stability, we will try to extend this approach to the‘lower symmetry’ solutions. In particular, we will outline aprocedure to exhaustively study the existence and stabil-ity of all these solutions. [1] L. M. Pecora, F. Sorrentino,A. M. Hagerstrom, T. E. Murphy, R. Roy, ”Cluster Syn-chronization and Isolated Desynchronization in ComplexNetworks with Symmetries”, Nature Communications, 5,

132 DS15 Abstracts

4079 (2014)

Francesco SorrentinoUniversity of New MexicoDepartment of Mechanical [email protected]

Aaron M. HagerstromUniversity of [email protected]

Louis M. PecoraNaval Research [email protected]


Rajarshi RoyUniversity of Maryland, College Park, MD, [email protected]

MS21

A Multi Agent Control Strategy for Sampling Un-certain Spatio-Temporally Varying Flow Fields

Uncertainties are a key factor when measuring geophys-ical flows to determine optimal positions for mobile sen-sors. To include uncertainties with a physical model of theenvironment, a model-based observer framework is used,which integrates measurements from sensors and propa-gates the estimated field by computational fluid dynamics.Spatiotemporal flow, concentration and uncertainty layersof this observer are combined with importance and colli-sion avoidance maps to generate optimal paths for a teamof underactuated autonomous sampling vehicles.

Axel HackbarthHamburg University of [email protected]

Edwin KreuzerInstitute of Mechanics and Ocean EngineeringHamburg University of [email protected]

MS21

Bayesian Nonlinear Assimilation for EulerianFields and Lagrangian Trajectories

We consider the Bayesian nonlinear assimilation of Eule-rian and Lagrangian flow data, exploiting nonlinear gov-erning equations and mutual information structures inher-ent to coastal ocean dynamical systems and optimally in-ferring the corresponding multiscale fields and transports.Our Bayesian nonlinear smoothing combines reduced-orderDynamically-Orthogonal equations with Gaussian MixtureModels, extending linearized backward pass updates to aBayesian nonlinear setting. This mutual information trans-fer, both forward and backward in time, is linked to La-grangian concepts, coherent structures and optimal sam-pling. Examples are provided with a focus on transports influid flows. This is joint work with Tapovan Lolla, PatrickHaley, Jing Lin, Deepak Subramani and our MSEAS group

at MIT.

Pierre [email protected]

MS21

Optimal Control in Lagrangian Data Assimilation

Inferring the state of an ocean flow is an integral part ofenvironmental monitoring. Autonomous vehicles with alimited capacity for locomotion are increasingly being usedfor data assimilation of various quantities of interest in theocean, including the underlying time-independent velocityfield. We assess the efficacy of optimal control techniquesto guide Lagrangian data assimilation in 2-dimensionalflows, focusing on assimilation of the velocity field itself.

Damon McdougallInstitute for Computational Engineering SciencesThe University of Texas at [email protected]

Richard O. MooreNew Jersey Institute of [email protected]

MS21

A Hybrid Particle-Ensemble Kalman Filter forHigh Dimensional Lagrangian Data Assimilation

We apply the recently proposed hybrid particle-ensembleKalman filter to assimilate Lagrangian data into a non-linear, high dimensional quasi-geostrophic ocean model.Effectively the hybrid filter applies a particle filter to thehighly nonlinear, low-dimensional Lagrangian instrumentvariables while applying an ensemble Kalman type updateto the high-dimensional Eulerian flow field. We will presentsome initial results and discuss both challenges and oppor-tunities that this strategy provides.

Elaine SpillerMarquette [email protected]

Laura SlivinskiWoods Hole Oceanographic [email protected]

Amit ApteTIFR Centre for Applicable MathematicsBangalore, [email protected]

MS22

The Geometry of the Toda Lattice Map

In this talk we consider some of the geometry behind theFlaschka coordinates for the Toda lattice equations. Weshow in particular that the Flaschka mapping is a momen-tum map and indicate how it can be generalized to studyrelated systems such as rigid body flows on lower triangu-lar matrices. This is joint work with Francois Gay-Balmazand Tudor Ratiu.

Anthony M. BlochUniversity of MichiganDepartment of Mathematics

DS15 Abstracts 133

[email protected]

MS22

Geodesic Finite Elements on Symmetric Spacesand Their Applications to Multisymplectic Varia-tional Integrators

To obtain multisymplectic discretizations of HamiltonianPDEs with symmetries, we introduce group-equivariantgeodesic finite-element spaces that take values in symmet-ric spaces. This is achieved by endowing symmetric spaces,and in particular, the space of positive-definite matrices,Lorentzian matrices, and symplectic matrices, with a Rie-mannian metric structure that is induced by a metric onthe general linear group. This allows us to apply the Rie-mannian center of mass construction to obtain manifold-valued shape functions.

Phillip GrohsETH ZurichSeminar for Applied [email protected]

Melvin LeokUniversity of California, San DiegoDepartment of [email protected]

Joe SalamonUniversity of California, San DiegoDepartment of [email protected]

John MoodyUniversity of California, San DiegoDepartment of [email protected]

MS22

Dynamics and Optimal Control of Flexible SolarUpdraft Towers

The use of solar chimneys for energy production has beensuggested more than 100 years ago but was hampered inlarge part due to the high cost of erecting tall towers. Re-cently, alternative technique of flexible towers built of in-flatable toroidal bladders was suggested. We develop a ge-ometric theory of motion and control of such towers, andreport on the results of experiments demonstrating the re-markable stability of the tower in real-life conditions.

Vakhtang PutkaradzeUniversity of [email protected]

MS22

Hamel’s Formalism for Infinite-Dimensional Me-chanical Systems

Hamel’s formalism is a form of Lagrangian mechanics thatgeneralizes both Euler-Lagrange and Euler-Poincare equa-tions. This is accomplished by unlinking the configurationand velocity measurements. The use of this formalism of-ten leads to a simpler representation of dynamics. This talkwill introduce Hamel’s formalism for infinite-dimensionalmechanical systems and demonstrate its utility in con-

strained dynamics.

Dmitry ZenkovNorth Carolina State UniversityDepartment of [email protected]

MS23

Self-Oscillations Via Two-Relay Controller: De-sign, Analysis, and Applications

Limit cycles induced by relay feedback systems and its ap-plication to underactuated mechanical systems will be ad-dressed. Particularly, a two-relay controller (TRC) is pro-posed for generation of Self-Oscillations (SO) in dynamicsystems. The design procedures are proposed using threemethodologies: the one based on DF, on Poincare maps,and on Locus of Perturbed Relay System method. Theresults are illustrated by experiments on SO generation ina wheel pendulum, Furuta pendulum, and a 3-DOF heli-copter.

Luis T. [email protected]

Igor BoikoThe Petroleum [email protected]

Leonid Fridman, Rafael IriarteUniversidad Nacional Autonoma de [email protected], [email protected]

MS23

Periodic Solutions in Dynamical Systems with Re-lay: Existence, Stability, Bifurcations

We consider a system of ordinary differential equationswith hysteresis of a relay type. In particular, such a sys-tem describes diffusion equations with hysteretic control onthe boundary. We analyze existence, stability, and bifur-cations of periodic solutions. Furthermore, we show thatadditional time-delay terms can favorably change the sta-bility of periodic solutions. The first part of our talk isbased on a joint work with Sergey Tikhomirov and thesecond part with Eyal Ron.

Pavel GurevichFree University [email protected]

MS23

Population Dynamics with the Preisach Operator

We consider population dynamics models where species(individuals) can switch between two modes of behaviorin response to exogenous stimuli. The switching rule ofeach individual is modeled by a two-threshold non-idealrelay; the averaged state of the individuals feeds back intothe system. We consider the SIR and predator-prey typemodels extended by these switching dynamics and discusscontinuous sets of equilibria, robust homoclinic trajectoriesand other dynamics.

Dmitry RachinskiyDepartment of Mathematical SciencesUniversity of Texas at Dallas

134 DS15 Abstracts

[email protected]

MS23

Reaction-Diffusion Equations with DiscontinuousRelay Nonlinearity

We consider reaction-diffusion equations involving a relaydiscontinuity in the source term, which is defined at eachspatial point. In particular, such problems describe chem-ical reactions and biological processes in which diffusiveand nondiffusive substances interact according to hystere-sis law. We show that behaviour of such systems essentiallydepends on the initial data. For the so-called transverseinitial data we show that solutions of the problem can bedescribed by a certain free boundary problem. In the caseof non-transverse initial data values of the relay form aspatially periodic or spatially quasyperiodic pattern thatoriginates at a point and propagates outwards.

Sergey TikhomirovMax Planck Institute for Mathematics in the ScienceChebyshev Laboratory, Saint-Petersburg State [email protected]

Pavel GurevichFree University [email protected]

MS24

Influence of Finite Larmor Radius on Critical Pa-rameters for Invariant Curves Break Up in AreaPreserving Maps Models of ExB Chaotic Transport

We consider 2-dimensional area preserving maps describ-ing chaotic transport in magnetized plasmas with zonalflows perturbed by electrostatic drift waves. We includefinite Larmor radius effects by gyro-averaging the corre-sponding Hamiltonians of the nontwist maps. Dynamicalsystems methods based on recurrence time statistics areused to quantify the dependence on the Larmor radius ofthe threshold for the destruction of shearless transport bar-riers.

Julio FonsecaUniversity of Sao [email protected]

Diego Del-Castillo-NegreteOak Ridge National [email protected]

Iber L. CaldasInstituto de Fsica, Universidade de So [email protected]

MS24

Breakup of Tori in Multiharmonic Nontwist Stan-dard Maps

Invariant circles play a prominent role in the dynamics ofarea-preserving maps. Unfortunately, much of the theorydeveloped to study these circles in twist maps does notapply to nontwist systems. In this talk we will employ aquasi-Newton, Fourier-based method to compute the con-jugacies of the circles. We will then demonstrate how thenear-critical conjugacies provide insight into the mechan-ics of the breakup of the circles and the topology of the

invariant sets afterwards.

Adam M. FoxDepartment of MathematicsWestern New England [email protected]


MS24

Nontwist Worm Map

In this work we propose a nontwist discrete map to inves-tigate how the confinement of chaotic regions affects thetopology of phase space. We choose to modify the Hamil-tonian that generates the standard nontwist map, in orderto create two linear barriers on the y-axis. As the perturba-tion is increased, we observe an onset of avoided regions notvisited by chaotic orbits initiated inside the range formedby the introduced barriers. On the other hand, unstablemanifolds from two hyperbolic fixed points, located out-side the chosen region, can pass through these barriers,filling the avoided regions generated by the confinementproposed. The effect that allows the diffusion of chaoticorbits in only certain directions is known as the ratchet ef-fect, which has been extensively studied in dissipative andHamiltonian systems, due to its relevance in biology andnanotechnology. The possible observation of the ratcheteffect in our map motivates our analyses.

Caroline G. L. MartinsInstitute for Fusion [email protected]

P. J. MorrisonDepartment of Physics and Institute of Fusion StudiesThe University of Texas at [email protected]

J. D. SzezechUniversidade Estadual de Ponta [email protected]

I. L. CaldasUniversidade de So PauloInstituto de [email protected]

MS24

Breakup of Shearless Tori and Reconnection in thePiecewise-Linear Standard Nontwist Map

A piecewise-linear version of the area-preserving stan-dard nontwist map is considered as a simple model of apiecewise-smooth map which also violates the twist con-dition. Using symmetry lines and involutions, I computeperiodic orbits to analyze periodic orbit collisions and sep-aratrix reconnection. The transition to chaos due to thedestruction of the shearless curve with rotation numberequal to the inverse golden mean is studied using Greene sresidue criterion.

Alexander WurmDepartment of Physical & Biological SciencesWestern New England University

DS15 Abstracts 135

[email protected]

MS25

The Role of Voltage-Dependent Electrical Couplingin the Control of Oscillations

We focus on the role of voltage-dependent electrical cou-pling in determining existence, stability and qualitativeproperties of solutions in the crab gastric mill rhythm.The network consists of a mutually inhibitory pair of neu-rons that receive electrical input from a particular projec-tion neuron together with the synaptic input from a pace-maker neuron. Using singular perturbation techniques andphase-plane space analysis, we derive and analyze a low-dimensional map that encodes the effects of these distinctinputs.

Christina MouserWilliam Patterson [email protected]

Farzan NadimNew Jersey Institute of Technology& Rutgers [email protected]

Amitabha BoseNew Jersey Inst of TechnologyDepartment of Mathematical [email protected]

MS25

The Essential Role of Phase Delayed Inhibition inDecoding Synchronized Oscillations

The widespread presence of synchronized neuronal oscilla-tions in the brain suggests the existence of a mechanismthat can decode such activity. Candidate mechanisms in-clude: high-spike threshold detection (HTD) and phase-delayed inhibition (PDI). Despite being more complex, PDIhas been observed in multiple systems, suggesting an in-herent advantage over the alternative. We show that PDIis capable of detecting synchrony far more robustly thanHTD, making the motif essential in any system with noisyencoders.

Badal JoshiCalifornia State University, San [email protected]

Mainak PatelCollege of William and [email protected]

MS25

Neural Mechanisms of Limb Coordination in Crus-tacean Swimming

Long-tailed crustaceans swim by rhythmically movinglimbs called swimmerets. Over the entire biological rangeof animal size and paddling frequency, movements of adja-cent swimmerets maintain an approximate quarter-periodphase difference with the more posterior limbs leading thecycle. Recently we have demonstrated that this frequency-invariant stroke pattern is the most effective and mechan-ically efficient paddling rhythm across the full range of bi-ologically relevant Reynolds numbers in crustacean swim-ming. Here, we argue that the organization of the neural

circuit underlying swimmeret coordination provides a ro-bust mechanism for generating this stroke pattern.

Tim LewisUniversity of California, [email protected]

MS25

Understanding and Distinguishing Multiple TimeScale Oscillations

CPGs may exhibit behavior, including bursting, involvingmultiple distinct time scales. Our goal is to understandbursting dynamics in multiple-time-scale systems, moti-vated by a model of respiratory CPG neuron. We ap-ply geometric singular perturbation theory to explain themechanisms underlying some interesting forms of burstingdynamics involving multiple forms of activity within eachcycle. We consider how many time scales are involved,obtaining some non-intuitive results, and identify solutionproperties that truly require three time scales.

Yangyang WangUniversity of [email protected]

Jonathan E. RubinUniversity of PittsburghDepartment of [email protected]

MS26

How Small a Thought: Design of Mixing and Sep-aration Processes with Dynamical Systems

We use dynamical systems to design manufacturing pro-cesses. Two examples are: (1) The Rotated Arc Mixer,an embodiment of the KAM theorem, increases manufac-turing productivity 25% and decreases mixing energy 95%.(2) The dynamical system for inertial particles in a laminarflow has both attracting and repelling regions, the interplayof which localizes particles when the Reynolds number ex-ceeds a critical value with applications in solid-liquid sep-arations. The predicted instability boundary agrees wellwith data.

Guy MetcalfeCSIRO Materials Science & EngineeringMelbourne, [email protected]

MS26

3D Chaotic Advection in Langmuir Cells

We investigate Lagrangian transport processes in a row ofhorizontally aligned, vertically sheared, alternating cylin-drical vortices: a simple model of ocean Langmuir circula-tions. We map out the chaotic regions and barriers that re-sult when the system is subject to three-dimensional steadyand unsteady disturbances. Chaotic advection occurs inresonant layers within each Langmuir cell, and exchangebetween the cells via three-dimensional turnstile lobes alsooccurs.

Larry PrattWoods Hole Oceanographic [email protected]

136 DS15 Abstracts

Irina RypinaWoods Hole Oceanographic [email protected]

MS26

Chaotic Mixing and Transport Barriers

We present experiments on chaotic transport in two- andthree-dimensional flows. The 2D flows are oscillating vor-tex chains with a wind that produces Levy flights and su-perdiffusive transport. We consider two 3D flows: (a) anested vortex chain flow, which gives rise to chaotic mix-ing even if the flow is time-independent; and (b) a vortexchain with Ekman pumping for which all transport barrierscan be destroyed even for arbitrarily small time-dependentperturbations.

Thomas H. SolomonDepartment of Physics & AstronomyBucknell [email protected]

MS26

Experimental Investigation of Fundamental La-grangian Transport Phenomena

Principal goal is experimental validation of the predictedresponse of a prototypical 3D unsteady flow with spheroidal(as opposed to toroidal) invariant surfaces to weak pertur-bations. Investigated are fundamental features as symme-tries and periodic lines in the unperturbed state and theformation of tubular structures upon weak perturbation.The latter promote global transport and, ultimately, 3Dchaos. Moreover, the experiments validate the essential in-dependence of this response upon the particular nature ofthe perturbation.

Michel SpeetjensLaboratory for Energy Technology, Dept. Mech. Eng.Eindhoven University of [email protected]

MS27

Dynamics of Asynchronous Networks

Systems that have the structure of a network of intercon-nected nodes are abundant in nature and technology. Manymathematical models of such networks are given as ordi-nary differential equations defined by smooth vector fields.These traditional or “synchronous’ network models, how-ever, fail to incorporate features seen in real world; forexample, individual components of a network cannot stopand restart in finite time. Asynchronous networks are anattempt to set up a mathematical framework to study sys-tems that exhibit stopping of nodes and their bifurcations.We compare our framework to traditional approaches ofdifferential equations with discontinuous vector fields andshow equivalence under certain assumptions. We also ex-plore deadlocks as specific dynamical states in which allnodes stop and never restart. These states cannot occurin a synchronous setup but are a natural feature of asyn-chronous settings.

Christian BickMax Planck Institute for Dynamics and Self-Organization:[email protected]

Michael Field

Imperial College LondonRice [email protected]

Anushaya MohapatraOregon State [email protected]

MS27

Pulse Bifurcations in Stochastic Neural Fields

We study the effects of additive noise on traveling wavesin spatially extended neural fields. Neural fields equationshave an integral term, characterizing synaptic interactionsbetween neurons at different spatial locations of the net-work. Traveling pulse solutions emerge when consideringthe effects of local negative feedback, generating a driftinstability. Near this criticality, we derive a stochastic am-plitude equation describing the pulse dynamics when thenoise and the deterministic instability are of comparablemagnitude.

Zachary KilpatrickUniversity of [email protected]

Gregory FayeEcole des hautes etudes en sciences [email protected]

MS27

Classifying Bifurcations in Coupled Cell Networks

Stewart and Golubitsky observed that robust synchronyin coupled cell networks is determined by quotient net-works. This result was recently generalized by DeVille andLerman, who noted that any so-called ‘graph fibration’ in-duces a conjugacy between the dynamics of a network andits quotients. Starting from the simple observation thatany ‘self-fibration’ hence induces a symmetry, we presenta theory of center manifold reduction that is specificallysuited for coupled cell networks.

Eddie Nijholt, Bob Rink, Jan SandersVU University [email protected], [email protected],[email protected]

MS27

Dynamics of Heterogeneous Networks: Reductionsand Coherent Behaviour

Recent experiments show that networks exhibit multiplelevels of coherent dynamics depending on the connectivitylevel of the network. Striking examples are found in thebrain. Indeed, synchronisation between highly connectedneurons coordinate and shape development in hippocampalnetworks. We provide a probabilistic approach for randomnetworks with chaotic dynamics. We develop a reductiontechnique to describe the dynamics of the highly connectednetwork layers in terms of the network’s microscopic de-tails.

Tiago PereiraDepartment of MathematicsImperial College, London, [email protected]

DS15 Abstracts 137

Matteo Tanzi, Sebastian van StrienImperial College [email protected], [email protected]

MS28

Oscillatory Dynamics of the Candelator

We describe the dynamics of the popular “candle see-saw”experiment in which a candle lit at both ends undergoesvertical oscillations as liquid wax drips from either end. Wecompare existing theory for small oscillations (θ < 30◦) andnumerical simulations for large oscillations to experimentaldata.

Greg A. Byrne, Mary Elizabeth Lee, Flavio FentonGeorgia Institute of [email protected], [email protected],[email protected]

MS28

Period Doubling in the Saline Oscillator

We provide today a simple, nonlinear system that capturesmany aspects of cardiac dynamics. The saline oscillator isa two chambered plastic box with one orifice connecting thetwo chambers. There is a jet of fluid flowing through theorifice. Along with this jet is a local voltage that parallelsthe flow of the jet. The voltage from the saline oscilla-tor highly resembles an action potential and can produceperiod one and period two cycles.

Diandian Diana ChenGeorgia Institute of TechnologySchool of [email protected]

Flavio FentonGeorgia Institute of [email protected]

MS28

Synchronization Patterns in Simple Networks ofOptoelectronic Oscillators

Simple motifs are important constituents of complex net-works; insight into the patterns of synchrony for differ-ent connection topologies is relevant to understanding howthey perform different dynamical functions. Global syn-chrony, the formation of clusters and desynchronized be-havior are all aspects of operation that are observed in theexperiments we describe on coupled optoelectronic oscilla-tors. We explore the dependence of these patterns of syn-chrony and their stability in relationship to the symmetriesof the network motifs.

Briana MorkUniversity of [email protected]

Kate CoppessUniversity of MichiganAnn Arbor, MI [email protected]

Caitlin R. S. WilliamsUniversity of MarylandDept. of [email protected]

Aaron M. Hagerstrom, Joseph HartUniversity of [email protected], [email protected]


Rajarshi RoyUniversity of [email protected]

MS28

Noise-Induced Transitions in Bistable TunnelDiode Circuits

We measure first-passage time distributions of electricalcurrent switching in a bistable tunnel diode circuit drivenwith adjustable noise intensity. Near a saddle-node bifur-cation, the logarithm of mean switching time scales linearlywith distance to the bifurcation point and inversely withnoise intensity. This suggests a noise-induced switchingprocess that is mediated by nucleation to a distinct stateof current flow, with nucleation occurring either at the edgeor interior of the diode.

Stephen Teitsworth, Yuriy Bomze, Steven Jones, RyanMcGeehanDuke [email protected], [email protected], [email protected], [email protected]

MS29

Population Models Applied to Model the Preg-nancy to Labor Transition

In human pregnancy the steroid hormone progesterone actsvia two receptors designated PR-A and PR-B. At termPR-A interferes with PR-B’s anti-inflammatory functionto initiate labor. We present a model of PR-B’s interac-tions with inflammation and use the dimensionless modelto predict the onset of labor in two human transcriptomedatasets. Solving the dimensionless model allows us to plotthe trajectory of a womans pregnancy in time and studythe dynamics of the PR-A/PR-B interaction.

Douglas BrubakerCWRU School of MedicineCenter for Proteomics and [email protected]


Mark ChanceCase Western Reserve UniversityCenter for Proteomics and [email protected]

Sam MesianoCase Western Reserve University Dept. of ReproductiveBiolog

138 DS15 Abstracts

[email protected]

MS29

Stochastic Fluctuations in Suspensions of Swim-ming Microorganisms

Mean field theories have had a good deal of success in ex-plaining many features regarding the remarkable dynamicsof suspensions of swimming microorganisms, including theonset of patterned motion in certain parameter regimes.We describe an extension of these mean field theories toinclude stochastic fluctuations in the density of the swim-ming microorganisms, and some computational issues insimulating the resulting stochastic partial differential equa-tions.

Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected]

Yuzhou QianRensselaer Polytechnic [email protected]

Patrick UnderhillRensselaer Polytechnic InstituteDepartment of Chemical and Biological [email protected]

MS29

A Model for Riot Dynamics: Shocks, Diffusion andThresholds

In this talk I will introduce variants of a system of differ-ential equations that model social outbursts, such as riots.The systems involves coupling of an explicit variable repre-senting the intensity of rioting activity and an underlying(implicit) field of social tension. Our models include the ef-fects of exogenous and endogenous factors as well as variouspropagation mechanisms. I will discuss various propertiesof this system, including the existence of traveling wavesolutions whose speed experiences a transition based on acritical threshold for the social tension.

Nancy Rodriguez-BunnUniversity of North Carolina at Chapel HillDepartment of [email protected]

Henri Berestycki, Jean-Pierre [email protected], [email protected]

MS29

Crowd Modeling: How Can People Respond toFear

We present a model for crowd dynamics where the motionof individuals is assumed to depend on their level of ex-citement (or fear) and thus the mechanism by which theemotion spreads play an important role. We start with anagent based Cucker-Smale-like model for which we derivethe continuity equation from the mean field limit and an-alyze their asymptotic behavior. Then we explore numeri-cally how variations, in both the effects of the emotion andits mechanism of propagation, affects the dynamics of the

crowd.

Jesus Rosado LinaresUniversidad de Buenos Aires - CONICETDepartamento de [email protected]


Andrea L. BertozziUCLA Department of [email protected]

MS30

A Self-Organising Distributed Strategy for OptimalSynchronisation of Networked Mechanical Systems

We consider the problem of adapting a weighted graph in adistributed fashion to maximise a desired cost function, asfor instance the algebraic connectivity of the graph subjectto constraints such as maximum weighted degree at eachnode and non-negativity of edge weights. The proposedmethod adapts edge weights in continuous time and is ro-bust to topological changes in the network. We apply thestrategy to solve the problem of optimising synchronisationin a network of coupled mechanical systems.

Louis Kempton, Guido HermannUniversity of Bristol, [email protected], [email protected]

Mario Di BernardoUniversity of BristolDept of Engineering [email protected]

MS30

Synchronization in Dynamical Networks of NoisyNonlinear Oscillators, Or Collective Behavior ofZebrafish

Zebrafish is a popular laboratory animal species for theinvestigation of several functional and dysfunctional bio-logical processes. Their burst-and-coast swimming style iswell described through a stochastic mean reverting jumpdiffusion model. Here, we analyze zebrafish schooling bymodeling their social interactions through a noisy vectorialnetwork model, in which each fish is assimilated to a net-work node whose neighbors are randomly and uniformly se-lected from the group. Through numerical simulations andclosed-form results, we assess the role of the network size,number of neighbors, and noise features on the stochasticsynchronization.

Violet Mwaffo, Ross AndersonDept. of Mechanical and Aerospace EngineeringNew York University Polytechnic School of [email protected], [email protected]

Maurizio PorfiriDept. of Mechanical, Aerospace and ManufacturingEngineeringPolytechnic University

DS15 Abstracts 139

[email protected]

MS30

Synchronization of a Nonlinear Beam Coupled withDeformable Substrates

The nonlinear dynamics of a distributed mechanical sys-tem comprised of a beam mechanically coupled with a de-formable substrate is considered. A mathematical modelof the coupled system is constructed with the inclusionof beam’s geometric nonlinearities and the combined ef-fect of strain and strain rate in the material response ofthe substrate. Synchronization between the beam and thesubstrate is formally investigated through the evolution ofthe governing system on nonlinear partial differential equa-tions. It is shown how locomotion of the beam can beachieved by synchronization with motions of the substrate,and how material and geometric properties of the substratecan be inferred by synchronization with imposed motionsof the beam.

Davide SpinelloUniversity of [email protected]

MS30

Synchronization Control of Electrochemical Oscil-lator Assemblies by External Inputs

We consider the manipulation of a collection of heteroge-neous nonlinear oscillators, which have unobservable stateand receive a common input, to form dynamical synchro-nization structures. Examining the conditions for entrain-ment of an oscillator to a periodic input yields insight intoa non-traditional control methodology. Phase coordinatetransformation, ergodic averaging, and novel waveform de-sign algorithms are used to produce inputs that establishstructures in the systems’ oscillation phases. The complex-ity of realizable designs is limited by the nonlinearity andheterogeneity of oscillators in the ensemble. The techniqueis applied successfully in experiments involving assembliesof electrochemical oscillators.

Anatoly ZlotnikWashington University in St. [email protected]

Istvan Z. KissDepartment of ChemistrySaint Louis [email protected]

Raphael NagaoSaint Louis [email protected]

Jr-Shin LiWashington University in St. [email protected]

MS31

Extreme Events on Small-World Networks of Ex-citable Units

We investigate small-world networks of excitable units thatexhibit different types of collective dynamics, which includeextreme events. The transitions between the different typesof dynamics are irregular and self-generated. We discuss

the mechanisms behind these transitions as well as the im-pact of the coupling topology on the observed phenomena.

Gerrit Ansmann, Klaus LehnertzDepartment of EpileptologyUniversity of Bonn, [email protected], [email protected]

Ulrike FeudelUniversity of OldenburgICBM, Theoretical Physics/Complex [email protected]

MS31

Extreme Events in Nature: Harmful Algal Blooms

Harmful algal blooms (HABs) are rare events in the oceancharacterized by a sudden large abundance of toxic phy-tolankton species. We study the mechanism behind theemergence of HABs by modeling the population dynamicsas an excitable system involving the competition betweendifferent activators, toxic and non-toxic species, as well thepreference of the inhibitor, the grazing zooplankton, forcertain activators. We show how toxin production, hydro-dynamics and variable nutrient input influence the triggermechanism.


Subhendu ChakrabortyDTU Aqua, [email protected]

Cornelius SteinbrinkUniversity Oldenburg, [email protected]

Rajat KarnatakTheoretical Physics/Complex Systems, ICBMUniversity [email protected]

Helmut HillebrandUniversity Oldenburg, GermanyICBM, [email protected]

MS31

Forecasting and Controlling Dragon-King Events inCoupled Dynamical Systems

It is often believed that extreme events in dynamical sys-tem follow a scale-free, power-law probability distributionand hence these events are unpredictable. We study ex-treme events in coupled chaotic oscillators and find thatthe largest events deviate from the power law distribution(so-called dragon-kings). We show that it is possible toforecast in real time an impending dragon-king and thatthey can be suppressed by applying tiny perturbations tothe system.

Daniel J. GauthierDuke [email protected]

140 DS15 Abstracts

Hugo CavalcanteDepartamento de InformaticaUniversidade Federal da [email protected]

Marcos OriaGrupo de Fisica Atomica e Lasers-DFUniversidade Federal da [email protected]

Didier SornetteDepartment of Management, Technology and EconomicsETH [email protected]

Ed OttUniversity of [email protected]

MS31

Extreme Events in Stochastic Multistable Systems

Pulses with extremely large amplitude appear in a systemwith coexisting attractors subject to stochastic processes.We demonstrate the emergence of such pulses in fiber andsemiconductor lasers close to saddle-node bifurcations, andshow how their probability depends on noise and laser pa-rameters.

Alexander N. PisarchikCentro de Investigaciones en [email protected]

Ricardo Sevilla-Escoboza, Guillermo Huerta-Cuellar,Rider Jaimes-ReateguiCentro Universitario de los LagosUniversidad de [email protected], [email protected],[email protected]

MS32

Convergent Heat Conduction in One-DimensionalLattices with Dissociation

The paper considers highly debated problem of conver-gence of heat conductivity in one-dimensional chains. Weconjecture that the convergence may be promoted due topossibility of the chain to dissociate. To clarify this point,we study the simplest model of this sort – a chain of linearlyelastic rods with finite size. Formation of gaps between therods is the only possible mechanism for scattering of theelastic waves. Heat conduction in this system turns out tobe convergent. Moreover, an asymptotic behavior of theheat conduction coefficient for the case of large densitiesand relatively low temperatures obeys simple Arrhenius-type law.

Oleg GendelmanTechnion Israel Institute of [email protected]

Alexander SavinInstitute of Chemical Physics, Moscow, [email protected]

MS32

Bistable Nonlinear Energy Sink Coupled System

for Energy Absorption and Harvesting

The nonlinear dynamics of a two-degree-of-freedom systemconsisting of a linear oscillator (LO) coupled to a bistablelight attachment (NES) is investigated. The parameters ofthe bistable NES are optimized in order to make it func-tioning as a linear TMD for low-amplitude, in-well, oscil-lations. The energy transfer mechanisms between the LOand the NES are discussed in order to assess the potential ofthis configuration for absorption and harvesting purposes.

Francesco RomeoUniversity of Rome - La [email protected]

Giuseppe HabibUniversity of [email protected]

MS32

Stochastic Closure Schemes for Bi-stable EnergyHarvesters Excited by Colored Noise

The goal of this work is the development of a closuremethodology that can overcome the limitations of tra-ditional statistical linearization/Gaussian closure schemesand can approximate the steady state statistical structureof bistable systems. Our approach is based on the mini-mization of a cost functional that expresses i) second-ordermoment information for the dynamics and ii) pdf represen-tation constraints for bi-stable systems. Our results com-pare favorably with direct Monte-Carlo simulations.

Themistoklis SapsisMassachusetts Institute of [email protected]

Han Kyul [email protected]

MS32

Acceleration of Charged Particles in the Presenceof Fluctuations

We consider resonances-driven acceleration and energytransport of charged particles in the earth magnetotail inthe presence of high-frequency fluctuations of the back-ground magnetic field. We show that fluctuations signifi-cantly affect both capture into resonance, by forcing parti-cles to escape from the surfatron resonance and thus alter-ing the resulting energy spectrum of particles; and scatter-ing by resonance, by changing the structure of beamlets,which are regular islands in chaotic sea.

Africa Ruiz Mora, Dmitri VainchteinDept. of Mechanical EngineeringTemple University, [email protected], [email protected]

MS33

Models of Large Deviations and Rare Events forOptical Pulses

In optical systems, amplified spontaneous emission noiseleads to errors if noise-induced fluctuations are large. Wediscuss methods for modeling large deviations in such sys-

DS15 Abstracts 141

tems. In particular, we show how the problem of find-ing large deviations can be formulated as a constrainedoptimization problem that combines the pulse evolutionequation and, in some cases, a detector model. The re-sults of the combined optimization are then used to guideimportance-sampled Monte-Carlo simulations to computeerror probabilities.

William KathDepartment of Applied Mathematics, NorthwesternUniversityDepartment of Neurobiology, Northwestern [email protected]

MS33

Influence of Periodic Modulation in Extreme Opti-cal Pulses

Semiconductor lasers with optical injection display a richvariety of behaviours, including extreme pulses, which havebeen identified as rogue waves (RWs). We have shown thatRWs can be completely suppressed via direct current mod-ulation, with appropriated modulation amplitude and fre-quency. Here we show that, when RWs are not suppressed,their probability depends on the modulation phase. Thereare “safe’ windows where no RWs occur. The most extremeRWs occur at the window boundary.

Cristina MasollerUniversitat Politecnica de Catalunya (UPCDepartament de Fsica i Enginyeria Nuclear (DFEN)[email protected]

MS33

Rare Events in Stochastic Dynamical Systems withDelay: From Random Switching to Extinctions

We consider delayed multi-attractor noise-induced switch-ing, and extinction in populations systems with delay nearbifurcation points. For weak noise, the rates of inter-attractor switching and extinction are exponentially small.Finding these rates is formulated as a set of acausal vari-ational problems, which in turn give the most probablepaths followed in switching or extinction. Explicit gen-eral theoretical results obtained show the analytical resultsagree well with the numerical simulations for both switch-ing and extinction rates.


Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]

Lora BillingsMontclair State UniversityDept. of Mathematical [email protected]

Mark DykmanMichigan State University

dykman at pa.msu.edu.

MS33

Rare Event Extinction on Stochastic Networks

We consider stochastic extinction of an epidemic on a net-work. We use a pair-based proxy model for nodes andlinks for a susceptible-infected-susceptible (SIS) epidemicon a random network. Extending the theory of large de-viations to random networks, we predict extinction timesand find the most probable path to extinction. Predictionsare shown to agree well with Monte Carlo simulations ofthe network.

Leah ShawCollege of William and [email protected]

Brandon S. LindleyNaval Research [email protected]


MS34

A Mathematical Model of Cancer Stem Cell Lin-eage Population Dynamics with Mutation Accumu-lation and Telomere Length Hierarchies

Cancer develops when cells acquire a sequence of muta-tions, which determines a hierarchy among the cells, basedon how many more mutations they need to accumulate inorder to become cancerous. Telomere loss and differenti-ation define another cell hierarchy, on top of which is thestem cell. This mutation-generation model combines themutation-accumulation hierarchy with the differentiationhierarchy of the cells, allowing us to take a step further inexamining cancer acquisition and growth.

Georgi KapitanovDepartment of MathematicsPurdue [email protected]

MS34

How Much and How Often? Mathematical Modelsof Cancer Vaccine Delivery

Cancer immunotherapy was heralded as the Breakthroughof the Year 2013 by Science magazine due to innovationsin strategies to harness the immune system to fight can-cer. Yet many questions remain unanswered: What is thecorrect mixture of therapies to give, in what order shouldthey be given, and according to what schedule? In thistalk I will present mathematical models that can be usedto suggest answers to these questions.

Ami RadunskayaPomona CollegeMathematics [email protected]

MS34

A Cell Population Model Structured by Cell Age

142 DS15 Abstracts

Incorporating Cell-cell Adhesion

An analysis is given of a continuum model of a proliferatingcell population, which incorporates cell movement in spaceand cell progression through the cell cycle. The modelconsists of a nonlinear partial differential equation for thecell density in the spatial position and the cell age coordi-nates. The equation contains a diffusion term correspond-ing to random cell movement, a nonlocal dispersion termcorresponding to cell-cell adhesion, a cell age dependentboundary condition corresponding to cell division, and anonlinear logistic term corresponding to constrained popu-lation growth. Basic properties of the solutions are proved,including existence, uniqueness, positivity, and long-termbehavior dependent on parametric input. The model isillustrated by simulations applicable to in vitro wound clo-sure experiments, which are widely used for experimentaltesting of cancer therapies.

Glenn WebbDepartment of MathematicsVanderbilt [email protected]

MS34

Mathematical Models of the Treatment of ChronicLymphocytic Leukemia with Ibrutinib and the De-velopment of Drug Resistance

Chronic lymphocytic leukemia (CLL) is the most commonleukemia in the western world. A recently developed tar-geted kinase inhibitor, ibrutinib, has shown very promisingresults in clinical trials and has now been approved for thetreatment of the disease. I will discuss mathematical mod-els that have been used to analyze the dynamics of CLLcells during drug therapy, and show how this model can beused to estimate parameters and obtain important insightsinto the mechanisms of action of the drug. Further, I willdiscuss mathematical models that seek to predict the dura-tion for which ibrutinib can maintain control of the disease,and when drug resistance causes relapse of the disease.

Dominik WodarzDept. of Ecology and Evolutionary BioUniversity of California, [email protected]

MS35

Inertia Effects in the Dynamics of Spherical andNon-Spherical Objects at Low Reynolds Number

Particles moving in a fluid at low but finite Reynolds num-bers experience hydrodynamic forces that may be signifi-cantly affected by fluid inertia. As a result the particle dy-namics (both translational and rotational) may be stronglyaltered. This presentation aims at presenting theoreticaltools, essentially based on matched asymptotic expansions,which allow to take these effects into account in certain sit-uations.

Fabien CandelierAix-Marseille [email protected]

MS35

Influence of the History Force on Inertial Parti-cle Advection: Gravitational Effects and Horizon-

tal Diffusion

We study the advection dynamics of inertial particles inorder to understand the sedimentation of marine snow. Inthis work we analyze the effect of the Basset force, an inte-gral over the particle’s history, on the advection of slowlymoving, dense or nearly neutral particles in the presenceof gravity. We highlight the parameters and select casestudies where memory changes the vertical and horizontaltransport.

Ksenia GusevaUniversity of Oldenburg, Theoretical Physics/ComplexSystemsOldenburg, [email protected]


Tamas TelEotvos Lorand University, Budapest, HungaryInstitute for Theoretical [email protected]

MS35

Effect of Fluid and Particle Inertia on the Dynam-ics and Scaling of Ellipsoidal Particles in ShearFlow

Simulations of the rotational behaviour of ellipsoidal par-ticles in linear shear flow are made by the Lattice Boltz-mann Method. As fluid and/or particle inertia is increased,a number of rotational states are observed and the bifur-cation sequence is detected and analysed. The behaviourof triaxial particles will be presented in some detail. Itis observed that the drift to chaotic rotation observed increeping flow seems to be less significant with fluid inertiapresent.

Tomas RosenKTH MechanicsRoyal Institute of [email protected]

Yusuke KotsuboTokyo [email protected]

Cyrus AidunG.W. Woodruff School of Mechanical EngineeringGeorgia Institute of [email protected]

Fredrik LundellKTH [email protected]

MS35

The Effect of Particle and Fluid Inertia on the Dy-namics of Particles in Flows

The dynamics of a very small particle suspended in a fluidflow is simple: the centre-of-mass is advected by the fluidvelocity, and the orientational dynamics is determined by

DS15 Abstracts 143

the sequence of fluid-velocity gradients that the particle ex-periences. For larger particles inertial effects may becomeimportant. Particle inertia is relatively straightforward totreat and there has recently been substantial progress inunderstanding its effect upon the dynamics of particles inflows. The effect of fluid inertia, by contrast, is more dif-ficult to describe. In this talk I will review what is knownabout the effect of fluid inertia upon the translational andorientational motion of particles in flows.

Bernhard MehligGothenburg UnivGothenburg, [email protected]

MS36

How Nonsmooth Are the Earth Sciences?

Geological folding of sedimentary rock layers is oftenthought of as being a smooth process, leading to regular si-nusoidal folds. In fact, a look at actual rocks will show youthat they often fold in a different non-smooth manner, withsharp corners. Such folding patterns include kink bandsand (zig-zag) chevron folds. Non-smooth features are of-ten linked to the presence of (possibly precious) mineralsdeep underground. In this talk I will develop a theory forsuch non-smooth behaviour which accounts for the frictionand compression between rock layers. This theory gives aconsistent description of the non-smooth folding patternsin terms of novel homoclinic bifurcations.

Chris BuddDept. of Mathematical SciencesUniversity of Bath, [email protected]

Tim J. DodwellBath Institute of Complex [email protected]

MS36

Analysis of an Arctic Sea Ice Model in a Nons-mooth Limit

We analyze an energy balance model for the Arctic, whichtakes the form of a low-dimensional, periodically forced dy-namical system that captures key feedbacks, in the limitof discontinuous ice-albedo feedback. This mathematicalsimplification enables detailed analysis and provides intu-ition for the role that the discontinuity boundary in phasespace plays in the bifurcation structure of the model. Weexplore how this analysis provides an alternative perspec-tive on previous numerical studies of this model.

Kaitlin HillEngineering Sciences and Applied MathematicsNorthwestern [email protected]

Mary SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]

MS36

Mathematical Quantifications of Resilience

Roughly speaking, resilience refers to the capacity of a sys-

tem to absorb disturbance and still retain its structure andfunction. This ecologically and socially relevant definitionof resilience is used in ecology, medicine, and climate sci-ence, and by policy makers in community, government andconservation efforts. Despite this fast growing interest inresilience across the sciences and social sciences, there islittle work done to describe resilience in quantifiable math-ematical terms. The Resilience Focus Group of the Mathe-matics and Climate Research Network is working on quan-tifiable definitions of resilience. A continuous dynamicalsystem is used to model the undisturbed ecological or bio-logical system, but what kind of perturbations best modeldisturbance to the system? How is resilience different fromLyaponov stability of the system? What metrics could weuse to understand this difference?

Alanna Hoyer-LeitzelMathematics DepartmentBowdoin [email protected]

MS36

The Search for Glacial Cycles: A Quasiperiodi-cally Forced Nonsmooth System in a ConceptualClimate Model

The glacial-interglacial cycle provides mesmerizing dynam-ical system and modeling topics. We present a novel en-ergy balance model with glacial mass balance adjustment.The model is a non-smooth dynamical system with non-autonomous orbital forcing, exhibiting a similar sawtoothresult typical of glacial and interglacial cycles. Some futuredynamical challenges will be outlined.

Esther WidiasihMathematics and Science SubdivisionUniversity of Hawai‘i West O‘[email protected]

James WalshOberlin [email protected]

Richard McGehee, Jonathan HahnUniversity of [email protected], [email protected]

MS37

Probabilistic Approach to Deployment Strategy inLagrangian Data Assimilation

A sequence of position observations by Lagrangian instru-ments, such as drifters and floats, contains time-integratedinformation of local flow velocity along the trajectories.Direct assimilation of these Lagrangian observations is ef-fective in estimating time-evolving, underlying flow. Alonga trajectory, each observation has a limited region of influ-ence where dynamic correlation to the observation locationis significant. Because trajectories are governed by the La-grangian geometry of the underlying flow, design of thedeployment strategy should take into account the detec-tion of the Lagrangian geometry. However, even when theunderlying flow is perfectly known, detection of the La-grangian geometry is challenging. In this talk, we presenta probabilistic approach to Lagrangian data assimilationthat incorporates the detection of the Lagrangian geom-etry while estimating the underlying flow and design the

144 DS15 Abstracts

deployment strategy accordingly.

Kayo IdeDept. of Atmospheric and Oceanic SciencesUniversity of Maryland, College [email protected]

MS37

A Quantitative Measure of Observability for DataAssimilations

For complicated systems found in numerical weather pre-diction, we introduce a characterization of observability toquantify the quality of information provided by sensors andprior knowledge. Optimal sensor positions can be found bymaximizing the observability. To evaluate the performanceof this method we consider the assimilation sensitivity ofthe optimized sensors as well as the performance in MonteCarlo experiments against test cases. Lastly we discuss theapplication of the method to mobile sensors.

Wei KangNaval Postgraduate SchoolDepartment of Applied [email protected]

Sarah King, Liang XuNaval Research [email protected],[email protected]

MS37

Multivehicle Motion Planning in the Presence ofOcean Eddies

We present a path-planning paradigm for a team of au-tonomous sampling platforms in the presence of coherentocean eddies. Vehicle paths near eddies are planned byutilizing Hamiltonian dynamics with added dissipation togenerate control vector fields for vehicle guidance. Thepath-planning framework is based on the concept of an ac-tive singularity whose strength is a tunable control input.The active singularities are associated with individual ve-hicles and the Hamiltonian structure of their dynamics en-ables a principled method for motion planning.

Frank D. LagorUniversity of MarylandDepartment of Aerospace [email protected]

Derek A. PaleyUniversity of MarylandDept. Aerospace Engineering and Inst. for [email protected]

MS37

Bayesian Nonlinear Smoothing and Mutual Infor-mation for Adaptive Sampling

New schemes are presented for optimal Bayesian nonlin-ear state estimation and adaptive sampling of nonlinearfluid and ocean dynamical systems, both forward and back-ward in time. The Bayesian nonlinear smoothing com-bines reduced-order Dynamically-Orthogonal (DO) equa-tions with Gaussian Mixture Models (GMMs), extendinglinearized backward pass updates to a Bayesian nonlinear

setting. Bayesian nonlinear adaptive sampling schemes arethen derived to predict the observations to be collectedthat maximize the mutual information about variables ofinterest. Examples are provided for fluid and ocean flows.This is joint work with our MSEAS group at MIT.

Tapovan Lolla, Pierre [email protected], [email protected]

MS38

A 3D Model of Cell Signal Transduction

We consider a 3D model of cell signal transduction in whichthe enzymes promoting the various stages in the signal arein fixed positions within the cell. We use the method ofmatched asymptotic expansions to reduce the partial dif-ferential equation modeling the signal transduction processto a system of ordinary differential equations. We considervarious bifurcations and the addition of delay to the sys-tem.

David IronDalhousie University, [email protected]

MS38

Organization of Metabolic Reactions for ImprovedEfficiency: Carbon Fixation and BioengineeringApplications

Recent advances in the experimental understanding of cel-lular organization motivate the need for novel spatial mod-eling of reactions in cells. Cells organize biochemical reac-tions to optimize growth, prevent toxic side-reactions, anddirect metabolic flux. We review recent experimental work,traditional methods for modeling metabolic networks, andopen problems. We present an example model of how theorganization of carbon fixation reactions in photosyntheticbacteria improves reaction efficiency reducing the energyneeded for growth of cells.

Niall M. ManganMassachusetts Institute of [email protected]

MS38

An Spatial Model of Anti-Cancer Drug Resistance:the Role of the Micro-Environment

Although resistance to chemotherapeutic agents seems tobe bound to appear, it is difficult to determine whether itarises prior to, or as a result of, cancer therapy. We devel-oped a hybrid discrete-continuous mathematical model toexplore anti-cancer drug resistance development. We de-scribe cells through a particle-spring approach respondingto changing levels of oxygen and drug concentrations, us-ing partial differential equations. We consider two kinds ofresistance (namely pre-existing and acquired) and explorethe role of microenvironmental niches of drug and oxygenin tumor cell survival and tumor expansion.

Kerri-Ann NortonJohns Hopkins UniversityDepartment of Biomedical [email protected]

Kasia RejniakH. Lee Moffitt Cancer Center & Research Institute

DS15 Abstracts 145

Integrated Mathematical [email protected]

Jana GevertzThe College of New [email protected]

Judith Perez-VelazquezHelmholtz Zentrum MunchenInstitute of Computational [email protected]

Zahra AminzareRutgers [email protected]

Alexandria VolkeningBrown Universityalexandria [email protected]

MS38

Synthetic Genetic Circuits for Spatial Patterning

One promise of synthetic biology is the creation of geneticcircuitry that enables the execution of logical programmingin living cells. Our lab has previously engineered intracel-lular and multicellular oscillators that give robust dynamicbehavior and observed them at the single cell and colonylevel using time-lapse microscopy. We have recently turnedto the task of creating a circuit giving robust spatial oscil-lations of gene expression in a population – stripes. Thekey to robust oscillations in temporal genetic oscillatorswas positive feedback coupled to delayed negative feed-back. In the spatial case, time delay corresponds to spatialoffset, suggesting that stripe formation will require localpositive feedback coupled to long-range negative feedback.This is essentially the model of pattern formation first de-scribed by Turing and expanded on by Gierer and Mein-hardt. These models as originally formulated require twosignals diffusing at very different rates, but similar pat-terning mechanisms can function even if the two signalsdiffuse at the same rate. Signals that do not crosstalk arerequired for these patterning mechanisms, but orthogonalsignals for synthetic genetic circuits have proved elusive.Recently we have developed a system that permits two sig-nals to be used in the same cell and her we describe effortsto construct self-organizing genetic circuits using this newtool.

Paul SteinerUniversity California San DiegoSan Diego, CA [email protected]

MS39

Reduced Models for Granular and Ecological Dy-namics

The potency of reduced dynamical models is illustratedwith two examples: First, by a sequence of reductions frominfinite-dimensional to discrete dynamical models of gran-ular flows. The effectiveness of these models for predictinggranular dynamics is demonstrated, as are some innovativeintegrability results they have inspired. Secondly, effectivereduced discrete dynamical models for ecological dynamicsare described and analyzed, and some associated serendip-itous insights on the identification and analysis of strange

attractors are outlined.

Denis BlackmoreNew Jersey Institute of TechnologyNewark, NJ 07102, [email protected]

Anthony RosatoNew Jersey Institute of TechnologyNewark, NJ 07102, [email protected]

Hao WuNew Jersey Institute of TechnologyNewark, NJ 07102 [email protected]

MS39

Collective Coordinates as Model Reduction forNonlinear Wave Interactions

The linear superposition of two traveling wave solutions ofa PDE offers a quantitative description of nonlinear waveinteractions, provided certain parameters, usually termed“collective coordinates”, of the shapes (e.g., the trajecto-ries of the centers) are considered unknown a priori. ForPDEs with Hamiltonian structure, substituting such anansatz into the Lagrangian leads to a reduced-order dy-namical model (a “coarse-grain” description) in the formof (a few) coupled nonlinear ODEs. To demonstrate theversatility of this variational technique, the sine–Gordonwave and the K∗(l, p) evolution equations are considered.

Ivan C. ChristovLos Alamos National [email protected]

MS39

On the Calogero Type Integrable Discretization ofNonlinear Dynamical Systems

The Calogero type matrix discretization scheme is appliedto constructing Lax type integrable discretizations of non-linear dynamical systems. The Lie-algebraic integrabilityproperties of co-adjoint flows on the related Markov typeLie algebras are discussed.

Anatolij PrykarpatskiAGH University of Science and Technology30-059 Krakow, [email protected]

MS39

A Scheme for Modeling and Analyzing the Dynam-ics of Logical Circuits

It is shown how logical circuits can be modeled by discretedynamical systems. While continuous dynamical systemsprovide quite accurate mechanistic models, they tend to becomputationally expensive to simulate. In contrast, sim-ulating a discrete dynamical system is relatively inexpen-sive. A model for the RS flip-flop circuit is constructedusing chaotic NOR gates. Next, a systematic - algorith-mic - first principles approach is developed and shown tobe useful in obtaining models of more complicated logicalcircuits.

Aminur Rahman

146 DS15 Abstracts

New Jersey Institute of [email protected]

MS40

Predator-Swarm Interactions

We propose a minimal model of predator-swarm interac-tions which captures many of the essential dynamics ob-served in nature. Different outcomes are observed depend-ing on the predator strength. For a weak predator, theswarm is able to escape the predator completely. As thestrength is increased, the predator is able to catch up withthe swarm as a whole, but the individual prey is able to es-cape by confusing the predator: the prey forms a ring withthe predator at the centre. For higher predator strength,complex chasing dynamics are observed which can becomechaotic, and eventually leading to successful prey capture.Our model is simple enough to be amenable to a full math-ematical analysis, which is used to predict the shape of theswarm as well as the resulting predatorprey dynamics as afunction of model parameters. The complex shape of theswarm in our model during the chasing dynamics is similarto the shape of a flock of sheep avoiding a shepherd.

Theodore KolokolnikovDalhousie [email protected]

MS40

Non-Standard Travelling Waves in Traffic andPedestrian Flow Models

Non-standard waves for particle models of car traffic andpedestrian flow are presented and analyzed both analyt-ically and numerically. The car traffic model is an ex-tended optimal velocity model with velocity dependentdriver strategies which shows traveling multi-pulse traf-fic jams and modulated waves. The pedestrian model isbased on a social force model with asymmetric couplings(pedestrians in front have bigger influence on the pedes-trian behaviour) and shows transitions to multi-lane wavesand peristaltic motion.

Paul CarterDivision of Applied MathematicsBrown Universitypaul [email protected]

Peter Leth ChristiansenDepartment of Applied Mathematics and ComputerScienceTechnical University of [email protected]

Yuri GaidideiBogolyubov Institute for Theoretical [email protected]

Carlos GorriaDepartment of Applied Mathematics and StatisticsUniversity of the Basque [email protected]

Christian MarschlerTechnical University of DenmarkDepartment of Mathematics and Computer [email protected]


Mads Peter SoerensenDepartment of MathematicsTechnical University of [email protected]

Jens StarkeTechnical University of DenmarkDepartment of [email protected]

MS40

Topological Data Analysis of Biological Aggrega-tion Models

We apply tools from topological data analysis to two math-ematical models inspired by biological aggregations suchas bird flocks, fish schools, and insect swarms. Our dataconsists of numerical simulation output from the modelsof Vicsek, et al. and D’Orsogna, et al.. These modelsare dynamical systems describing the movement of agentswho interact via alignment, attraction, and/or repulsion.Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure ofthese point clouds, interpreting the persistent homologyby calculating the first few Betti numbers. These Bettinumbers count connected components, topological circles,and trapped volumes present in the data. To interpretour results, we introduce a visualization that displays Bettinumbers over simulation time and topological persistencescale. We compare our topological results to order param-eters typically used to quantify the global behavior of ag-gregations, such as polarization and angular momentum.The topological calculations reveal events and structurenot captured by the order parameters.

Chad M. TopazMacalester [email protected]

Lori Ziegelmeier, Tom HalversonDept. of Mathematics, Statistics, and Computer ScienceMacalester [email protected], [email protected]

MS40

Modeling Stripe Formation in Zebrafish

Zebrafish is a small fish with distinctive black and yel-low stripes that form due to the interaction of differentpigment cells. We present a comprehensive agent-basedmodel for stripe formation in zebrafish that describes thefull spectrum of biological data: development from a larvalpre-pattern, ablation experiments, and mutations. We findthat fish growth shortens the necessary scale for long-rangeinteractions and that iridophores, a third type of pigmentcell, maintain stripe boundary integrity.

Alexandria VolkeningBrown Universityalexandria [email protected]

Bjorn SandstedeDivision of Applied Mathematics

DS15 Abstracts 147

Brown Universitybjorn [email protected]

MS41

Stability of Power Grid: Dynamical Systems Per-spective

Power grids can be conveniently represented as dynamicalsystems. Their normal operations depend on two kinds ofstability: steady state and transient stability. An overviewof the techniques for estimation of both types of stabilitywill be given. An approach for improving the stabilitybased on using electrical vehicles plugged to the grid willbe presented. Influence of the delays on the stabilizationwill be also shown.

Andrej GajdukMacedonian Academy of Sciences and Arts, Skopje,[email protected]

Mirko TodorovskiSs Cyril and Methodius University, Faculty of [email protected]

Lasko BasnarkovMacedonian Academy of Sciences and [email protected]

Ljupco KocarevUniversity of California, San DiegoInstitute for Nonlinear [email protected]

MS41

Analysis of Systems in Buildings Using KoopmanOperator Methods

Commercial buildings consume 20% of U.S. energy halfof which is due to Heating, Ventilation, & Air Condition-ing. Due to the multiple time-scales and spatial configu-rations of HVAC sub-systems, energy efficiency is difficultto achieve. By projecting building time-series data ontoeigenmodes of the Koopman operator, interactions betweensub-systems become identifiable leading to improved build-ing performance. Technique is illustrated on model simu-lated predictions and actual sensor data.

Michael GeorgescuUniversity of California, Santa [email protected]

MS41

Time Series Prediction for Renewable Energy Re-sources

The prediction of renewable energy outputs is almostequivalent to weather forecasting, although the time reso-lutions often required are different between these two: theprediction of renewable energy often needs the finer reso-lution that can go down to the orders of seconds and min-utes. The prediction of renewable energy outputs of sucha finer resolution can be realized by employing time seriesprediction with empirical observations rather than refiningoutputs of global circulation models.

Yoshito Hirata

Institute of Industrial ScienceThe University of [email protected]

Kazuyuki AiharaJST/University of Tokyo, JapanDept of Mathematical [email protected]

Hideyuki SuzukiUniversity of [email protected]

MS41

Hierarchical Subsystem Clustering for DistributedControl of Networked Systems

We examine hierarchical subsystem clustering for net-worked systems in the framework of hierarchical dis-tributed control proposed by the authors. More specifi-cally, for various existing clustering methods such as theK-means method, we numerically examine stability as wellas control performance of the whole control system withresultant subsystem clusters. This study is expected to bea first step towards development of hierarchical distributedcontrol theory with systematic determination of subsystemclustering.

Tomonori Sadamoto, Takayuki Ishizaki, Jun-ichi ImuraTokyo Institute of [email protected], [email protected],[email protected]

MS42

On the Relationship Between Koopman Mode De-composition and Dynamic Mode Decomposition

We present an explicit relationship between KoopmanMode Decomposition (KMD) of dynamical systems andcompanion-matrix version of Dynamic Mode Decomposi-tion (DMD).We use this relationship to explain some of thedifferences in the variants of DMD algorithm. We also dis-cuss some applications of DMD as a tool to extract Koop-man modes from experimental and computational data.

Hassan ArbabiUC Santa [email protected]

Igor MezicUniversity of California, Santa [email protected]

MS42

Extracting Spatial-Temporal Coherent Patterns inLarge-Scale Neural Recordings Using DynamicMode Decomposition

There is a broad need in the neuroscience community tounderstand and visualize large-scale recordings of neuralactivity, big data acquired by tens or hundreds of electrodessimultaneously recording dynamic brain activity over min-utes to hours. Such dynamic datasets are characterized bycoherent patterns across both space and time, yet existingcomputational methods are typically restricted to analy-sis either in space or in time separately. Here we reportthe adaptation of dynamic mode decomposition (DMD),an algorithm originally developed for the study of fluid

148 DS15 Abstracts

physics, to large-scale neuronal recordings. We validatedthe DMD approach on sub-dural electrode array recordingsfrom human subjects performing a known motor activationtask. Next, we leveraged DMD in combination with ma-chine learning to develop a novel method to extract sleepspindle networks from the same subjects. We suggest thatDMD is generally applicable as a powerful method in theanalysis and understanding of large-scale recordings of neu-ral activity.

Bing W. BruntonUniversity of [email protected]

MS42

Dynamic Mode Decomposition with Control witha Special Focus on Epidemiological Applications

Here, we present a new method called Dynamic Mode De-composition with control (DMDc) which, similar to Dy-namic Mode Decomposition (DMD), finds low-order mod-els from high-dimensional, complex systems, but now in-corporates the effect of external control. In contrast toDMD, DMDc is capable of producing an accurate input-output model recovering the dynamics and modes withoutbeing corrupted by external forcing. We focus on a setof epidemiological applications which have both dynamicsand interventions (control).

Joshua L. ProctorIntellectual [email protected]

MS42

A Rigorous Definition and Theory of DynamicMode Decomposition

Dynamic mode decomposition (DMD) is often describedalgorithmically, rather than through a set of defining math-ematical properties, as other decompositions are. In thistalk, we present a formal definition of DMD that agreeswith the familiar algorithmic descriptions. This establishesa foundation from which new theory and algorithms canbe developed. For instance, it allows for non-sequentialdatasets and elucidates the connections between DMD,Koopman operator theory, the eigensystem realization al-gorithm, and linear inverse modeling.

Jonathan H. TuUC [email protected]

Clarence RowleyPrinceton UniversityDepartment of Mechanical and Aerospace [email protected]

MS43

Methods for Implementing Exactly Solvable Chaosin Electronic Circuits

Exactly solvable chaos may lend many advantages to ap-plications in radar, communications, computing and secu-rity. In order for these technologies to benefit from the useof exactly solvable chaos, these governing equations mustbe first implemented using various electronic circuit de-sign techniques. This work outlines various methodologiesfor realizing exactly solvable chaos using mixed-signal elec-

tronic circuits, while considering many crucial componentdesign limitations such as frequency response, bandwidth,noise, linearity and parasitics.

Aubrey N. Beal, Robert DeanAuburn [email protected], [email protected]

MS43

A Pseudo-Matched Filter for Solvable Chaos

In the work of Corron et al. [Chaos 20, 023123 (2010)],a matched filter is derived for the chaotic waveforms pro-duced by a piecewise-linear dynamical system. Motivatedby these results, we systematically investigate the matchedfilters properties in order to design a pseudo-matched fil-ter, which captures important features of the matched fil-ter and is realized using first order filters. Using numericalsimulations and statistical analyses, we compare the per-formances of the matched and pseudo-matched filters.

Seth D. CohenDucommun MiltecHuntsville, [email protected]

MS43

Communication Waveforms and Exactly SolvableChaos

We show that, under practical constraints, an optimal com-munication waveform is chaotic. That is, we assume asimple matched filter and derive the corresponding basisfunction that maximizes the receiver signal-to-noise per-formance. We then consider a communication waveformusing this basis function, and surprisingly we find a wave-form return map that is conjugate to a chaotic shift map.We also show a relationship of the optimal waveform toan exactly solvable hybrid chaotic oscillator that has beenpreviously reported.

Ned J. CorronU.S. Army [email protected]

Jonathan N. BlakelyUS Army [email protected]

MS43

Exactly Solvable Chaos in An ElectromechanicalOscillator

A novel electromechanical chaotic oscillator is describedthat admits an exact analytic solution. The oscillator isa hybrid dynamical system with governing equations thatinclude a linear second order ordinary differential equa-tion with negative damping and a discrete switching con-dition that controls the oscillatory fixed point. The systemproduces provably chaotic oscillations with a topologicalstructure similar to either the Lorenz butterfly or Rossler’sfolded-band oscillator depending on the configuration. Ex-act solutions are written as a linear convolution of a fixedbasis pulse and a sequence of discrete symbols. We findclose agreement between the exact analytical solutions andthe physical oscillations. Waveform return maps for bothconfigurations show equivalence to either a shift map or

DS15 Abstracts 149

tent map, proving the chaotic nature of the oscillations.

Lucas IllingReed [email protected]

MS44

A Measurable Perspective on Finite Time Coher-ence

The concept of coherent structures in a flow refers to no-tions of subsets of the flow which preserve some measurablequantity, despite the generally nonlinear flow: somethingsimple embedded in the complexity. Our own perspectiveof shape coherent sets is defined in terms of flow that islocally as rigid body motions, and uncovered by investi-gating boundary curvature evolution. Key for unifying toother concepts of coherence is choice of measure interpretedacross domains .


Tian MaDepartment of Mathematics and Computer ScienceClarkson [email protected]

MS44

Rigorous Numerical Approximation of InvariantMeasures – History and Recent Progress

Interest in rigorous schemes to approximate invariant mea-sures in ergodic theory dates back at least to Ulam’s cel-ebrated 1960 conjecture about their approximation viafinite-dimensional Markov chains. We review this historyfrom the modern perspective of spectral perturbation. Re-cently, with R. Murray, convex optimization techniqueshave been proposed; we compare and contrast these withUlam’s scheme. Finally, we place all of these approachesinto a unified setting of regularized least-squares optimiza-tion for solution of the (ill-posed) Perron-Frobenius fixedpoint problem.

Chris BoseMathematics and StatisticsUniversity of Victoria, [email protected]

MS44

Non-Autonomous Dynamical Systems, Multiplica-tive Ergodic Theorems and Applications

Non-autonomous dynamical systems yield very flexiblemodels for the study of time-dependent systems, with driv-ing mechanisms ranging from deterministic forcing to sta-tionary noise. Multiplicative ergodic theorems (METs) en-compass fundamental information for the study of trans-port phenomena in such systems, including Lyapunov ex-ponents, invariant measures and coherent structures. Inthis talk, we will discuss recent developments on METs,motivated by questions coming from oceanic and atmo-spheric dynamics.

Cecilia Gonzalez TokmanSchool of Mathematics and StatisticsUniversity of New South [email protected]

Gary FroylandUNSW [email protected]

Anthony QuasUniversity of [email protected]

MS44

On Triangularization of Matrix Cocycles in theMultiplicative Ergodic Theorem

The Multiplicative Ergodic Theorem shows that a real ma-trix cocycle is block diagonalizable over the real numbers,given mild hypotheses; that is, the cocycle is cohomologousto one in which the matrices are supported on blocks corre-sponding to the Lyapunov exponents. We shall talk aboutblock triangularizing cocycles, and investigate when thismay occur; namely, not all cocycles may be triangularized,even over the complex numbers.

Joseph HoranDepartment of Mathematics and StatisticsUniversity of [email protected]

MS45

Vibration Energy Harvesting Based on NonlinearTargeted Energy Transfer

We investigate the use of targeted energy transfer via es-sential (nonlinearizable) stiffness nonlinearity to promoteefficient energy harvesting. The system of interest consistsof two oscillators, a linear primary and strongly nonlinearsecondary, coupled electromechanically. The primary is agrounded linear oscillator; the secondary, the harvester,is a lightweight oscillating mass attached to the primarymass through a permanent magnet, inductance coil, anduntensioned steel wire positioned normal to the directionof the oscillation, which provides the purely cubic essentialnonlinearity. Impulsive excitation of the primary at a suf-ficiently high level results in transient resonance capturewith the secondary, resulting in a large-amplitude high-frequency component in the harvester response. Energygenerated is harvested in a circuit via the magnet and coil.Performance is demonstrated through both simulation andexperiment.

Kevin RemickDepartment of Mechanical Science and EngineeringUniversity of Illinois - Urbana- [email protected]

D Dane QuinnUniversity of AkronDept of Mechanical [email protected]

D. Michael McFarlandUniversity of [email protected]

Lawrence BergmanUniversity of Illinois - Urbana - [email protected]

Alexander VakakisUniversity of Illinois

150 DS15 Abstracts

[email protected]

MS45

Nonlinear Energy Harvesting in Granular Media

In this talk, we explore the possibility of using granularcrystals for the purpose of vibration energy harvesting.In particular, we focus on time-periodic structures of suchsystems and how the interplay of spatial heterogeneity, dis-creteness and nonlinearity can lead to desirable localizationproperties. We approach the problem with computational,analytical and experimental tools.

Christopher ChongETH [email protected]

MS45

2D Energy Channeling in the Locally ResonantAcoustic Metamaterials

Dynamics of locally resonant, acoustic meta-materials is asubject of intense study of the past few years. As of todaythere is a lack of a substantial theoretical understandingof the dynamics of locally resonant, 1D, 2D non-linear lat-tices. In the present talk I’ll present the recent results ofthe theoretical study of controlled, unidirectional energytransport, wave redirection and nonlinear energy channel-ing in the locally resonant, 2D metamaterials, incorporat-ing internal rotators.

Yuli StarosvetskyTechnion, Israel Institute of [email protected]

Kirill VorotnikovFaculty of Mechanical EngineeringTechnion - Israel Institute of [email protected]

MS45

Non-Linearizable Wave Equation: Nonlinear SonicVacuum

We consider low-energy oscillations of a finite spring-masschain in the plane, with geometric nonlinearity generatinga smooth nonlinear sonic vacuum with zero speed of sound,and strongly non-local nonlinear terms despite only next-neighbor physical interactions between particles. The non-linear normal modes of this system are identical to thoseof a simple linear spring-mass chain. Asymptotic analy-sis reveals a rich structure of resonance manifolds, mixedstanding/traveling waves, and strong nonlinear energy ex-changes between modes.

Leonid ManevichSemenov Institute of Chemical PhysicsRussian Academy of [email protected]

Alexander VakakisUniversity of Illinois

[email protected]

MS46

The Effect of Extrinsic Noise on Gene Regulation

Stochastic gene expression is influenced both by intrinsicnoise (IN) arising from intracellular variability and extrin-sic noise (EN) arising from intercellular variability. WhileIN is well understood, a rigorous understanding of how ENinfluences the function of genetic networks is still lacking.Here we study the IN/EN interplay in simple network mo-tifs, focusing of how EN characteristics affect the overallstatistics. Our analytical predictions are compared withMonte-Carlo simulations efficiently accounting for fluctu-ating reaction rates.

Michael AssafRacah Institute of PhysicsHebrew University of [email protected]

MS46

Fundamental Limits to the Precision of Multicellu-lar Sensing

Single cells sense their environment with remarkable pre-cision. At the same time, cells communicate. How aresensing and communication related? I will describe a sys-tem in which epithelial cells, by communicating, can detectshallower chemical gradients than single cells can alone. Aminimal stochastic model provides fundamental limits onthe precision of communication-aided sensing, which wevalidate in the experimental system. Our results demon-strate that known sensory limits are altered when commu-nication is accounted for.

Andrew MuglerDepartment of Physics and AstronomyPurdue [email protected]

Matthew BrennanJohns Hopkins [email protected]

Andre LevchenkoYale [email protected]

Ilya NemenmanEmory [email protected]

MS46

Inferring Predictive Signal-Activated Gene Regu-lation Models from Noisy Single-Cell Data

Spatial, temporal and stochastic fluctuations can cause ge-netically identical cells to exhibit wildly different behav-iors. At first glance, fluctuations seem to compromise cel-lular responses, complicate modeling, and disrupt predic-tive understanding and control. Under closer examination,cellular fluctuations actually become exceptionally useful.I will discuss how integrating single-cell experiments withprecise spatiotemporal stochastic analyses can reveal newinsight, enable quantitatively predictive models, and im-prove the controllability of heterogeneous gene regulation

DS15 Abstracts 151

in bacteria, yeast and mammalian systems.

Brian MunskyCollege of EngineeringColorado State [email protected]

MS46

Coarse-Graining Biochemical Networks

We consider a generic stochastic model either for ion trans-port through a single channel with arbitrary internal struc-ture or arbitrary enzyme kinetics. We show that mea-surements of statistics of transition times through specificstates of such a system contain only restricted informa-tion about parameters of the model. This observation al-lows one to identify the most relevant variables that canbe quickly estimated if statistical measurements are per-formed on a biochemical process at a single molecule level.For example, we show that the Poisson indicator in enzymekinetics depends only on three parameters in addition tothe parameters of the Michaelis-Menten curve that charac-terizes average enzyme turnover rate in a very broad classof enzyme models. Nevertheless, measurement of Poissonindicator or Fano factor for such renewal processes can dis-criminate reactions with multiple intermediate steps as wellas provide valuable information about the internal kineticrates.

Nikolai SinitsynTheoretical divisionLos Alamos National [email protected]

MS47

Computation of the Koopman Eigenfunctions Is aSystematic Method for Global Stability Analysis

The Koopman operator framework provides a novel ap-proach to global stability analysis of dynamical systems,which can be seen as an extension of classic stablility analy-sis of linear systems. We show that the existence of specificeigenfunctions of the operator is a necessary and sufficientcondition for global stability of the attractor. Moreover,the computation of the eigenfunctions in a polynomial ba-sis yields systematic methods for stability analysis and es-timation of the basin of attraction.

Alexandre Mauroy, Igor MezicUniversity of California, Santa [email protected], [email protected]

MS47

Koopman Mode Expansion in Theory and Practice

We discuss current theory and practice of applications ofKoopman operator methods in dynamical systems and itsrelationship with computational methods. The approachhas recently been extended to associate geometrical ob-jects such as isochrons and isostables with level sets ofKoopman eigenfunctions. We will also discuss the relation-ship between numerical methods such as Dynamic ModeDecomposition and Koopman Mode Decomposition, andextensions of theory to stability of nonlinear systems andcontrol.

Igor MezicUniversity of California, Santa Barbara

[email protected]

MS47

Generalized Laplace Analysis and Spaces of Ob-servables for the Koopman Operator

We extend Koopman spectral analysis to spectral operatorsof scalar type having non-unimodular spectrum and giveconditions on the spectrum so that spectral projections canbe computed using Laplace averages. This naturally ex-tends the theory existing for dynamical systems restrictedto an attractor, where spectral projections are computedusing Fourier averages, to dissipative systems. For dynam-ical systems with dissipation, we construct a natural spaceof observables for which the associated Koopman operatoris spectral.

Ryan MohrUniversity of California, Santa [email protected]

MS47

What Can the Koopman Operator Do for Dynam-ical Systems?

We report on ”Operator Theoretic Aspects of Ergodic The-ory” as developed in the new monograph with the samename (Springer 2015, coauthored by Tanja Eisner, BalintFarkas, Markus Haase and R.N.) and their applications tononlinear dynamical systems.

Rainer NagelUniversity of [email protected]

MS48

An Observational Basis for Sudden StratosphericWarmings As Bifurcations in Planetary Wave Am-plitude

Sudden stratospheric warmings (SSWs) are midwinterevents in which the polar cap temperature and circulationundergo large and abrupt changes. Currently two compet-ing theories contend to explain the explosive stratosphericwave amplitude growth that triggers a SSW: anomalouslylarge planetary wave forcing, or nonlinear resonance. Inthis work we utilize 35 years of atmospheric data to showthat SSWs are most likely triggered by a wave amplitudebifurcation due to nonlinear resonance.

John R. AlbersCIRES, University of ColoradoNOAA/ESRL Phys. Sci. [email protected]

MS48

Tropical-Extratropical Wave Interactions in theAtmosphere

The coupling between moist convective processes and large-scale circulation is at the core of tropical-extratropical at-mospheric interactions. Observational evidence of this typeof phenomena will be presented and a reduced model willbe proposed to understand the physical processes underly-ing this type of multi-scale interactions. In particular, themodel will be used to interpret the relative roles of trop-ical versus extratropical wave sources of moist convection

152 DS15 Abstracts

modulations at low latitudes.

Juliana DiasNOAA Earth System Research [email protected]

MS48

The Use of Green Functions of the Shallow WaterModel for Understanding Climate Anomalies

Climate anomalies are frequently connected the intensityand positioning of anomalous tropical heat sources. GreenFunctions of simplified atmospheric models constitute asimple tool for identifying the origin of major climateanomalies. Examples will be shown for the 2014 climateanomalies such as the North American extreme cold period,the flooding in western Europe and the warm conditions ineastern Europe, and the extreme drought in SoutheasternSouth America that caused severe water shortage.

Pedro Leite da Silva DiasLaboratorio Nacional de Computacao Cientifica, BrazilIAG, University of Sao Paulo, [email protected]

MS48

The Role of Noise in Bifurcations in Fluids and theAtmosphere

Triggering the strongest disturbances to the wintertimestratospheric polar vortex sudden stratospheric warming(SSWs) is to first order governed by the strength of forcingdue to planetary-scale atmospheric waves and the vortexswaveguide. Using a model of SSWs, stochastic Kida vortexequations, we show that the basin of attraction is not onlymore complex than previously believed, but can be signifi-cantly altered by additive noise. Resulting soft bifurcationcaused by the random basin is the possible mechanism lead-ing to a SSW.

Yuzuru SatoRIES, Hokkaido [email protected]

David J. AlbersColombia UniversityBiomedical [email protected].

MS49

Dangerous Border Collision Bifurcation in Piece-wise Smooth Maps

A dangerous bifurcation has been defined as a situationwhere a stable period-1 orbit occurs before and after thebifurcation, and yet the basin of attraction shrinks to zerosize at the bifurcation point. It is known that this phe-nomenon can occur is non-smooth systems. In this paperwe generalize the definition to one in which any attract-ing orbit may exist before and after the bifurcation, andtheir basins of attraction shrink to zero size at the bifurca-tion point, resulting in divergence of orbits starting fromall initial conditions. Using the normal form of a 2D piece-wise smooth map, we develop the conditions and show theparameter space regions where this phenomenon occurs.

Soumitro BanerjeeIndian Institute of Science education & Research,Kolkata, India

[email protected]

Arindam SahaIISER Kolkata, [email protected]

Viktor AvrutinIPVSUniversity of [email protected]

Laura GardiniUniversity of UrbinoDepartment of Economics, Society and [email protected]

MS49

Generalized Hopf Bifurcation in a NonsmoothClimte Model

Low dimensional ocean circulation box models have beenused by many scientists to model large scale behavior inocean dynamics. The convection box model we will dis-cuss in this talk exhibits oscillitory behavior, and so wasinfluential to the field at its time of publication. The modeldepends on abrupt transitions between two different mixingstates, and has a natural nonsmooth limit. In this talk wediscuss the Hopf bifurcation in the smooth model, and itscontinuation to the nonsmooth limit. We will also discussgeneral forms for this type of nonsmooth Hopf bifurcation.

Julie LeifeldUniversity of [email protected]

MS49

Canard Phenomena in Nonsmooth Systems

This presentation will present new results on canard phe-nomena in planar nonsmooth systems. Canard explosionin piecewise-smooth, continuous, planar systems will bediscussed, including the super-explosion phenomenon. Ad-ditionally, the talk will touch on canard trajectories in dis-continuous systems. It will be shown that it is possiblefor a discontinuous system to undergo a canard explosion,where part of the stable canard cycle is a Filippov slidingsolution.

Andrew RobertsDepartment of MathematicsThe University of North Carolina at Chapel [email protected]

MS50

Intrinsic Mechanisms for Pattern Generation inThree-Node Networks

Bursting patterns can be qualified and modeled using low-dimensional models. We show that, depending on intrin-sic mechanisms of release, escape, and post-inhibitory re-bound, reciprocally inhibitory Fitzhugh-Nagumo type net-works can produce a range of phase-locked states suchas anti-phase bursting, propagating waves, and peristalticpatterns with recurrently phase-varying lags. Phase-lagreturn maps identify phase states with rhythm switchingand attractor robustness revealed using external inhibition.

DS15 Abstracts 153

Our qualification promotes the use of simplified modelingfor CPG circuitries.

Jarod CollensGeorgia State UniversityNeuroscience Institute and Mathematics [email protected]

Aaron [email protected]

Deniz AlacamGeorgia State UniversityMathematics [email protected]

Tingli XingGeorgia State [email protected]

Drake KnapperGeorgia State [email protected]

Justus T. SchwabedalNeuroscience InstituteGeorgia State [email protected]

Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]

MS50

From Andronov-Hopf to Z3 Heteroclinic Bifurca-tions in Cpgs

We study the formation of some rhythmic states in vari-ous 3-cell network motifs of a multifunctional central pat-tern generator (CPG) via several computational tools.The study is complemented with a detailed analysis ofa single leech heart neuron, including bifurcations, spike-counting techniques and Lyapunov exponents, that givesa “roadmap” for the basic neuron. We locate a completeroute of Andronov-Hopf and heteroclynic cycle connectionsin the 3-cell leech heart neurons and we illustrate the useof advanced GPU computing technologies and suitable nu-merical algorithms.

Marcos RodriguezCentro Universitario de la [email protected]

Roberto Barrio, Sergio SerranoUniversity of Zaragoza, [email protected], [email protected]


MS50

Key Bifurcations of Bursting Polyrhythms in 3-Cell

Central Pattern Generators

We identify and describe the key qualitative rhythmicstates in various 3-cell network motifs of a multifunctionalcentral pattern generator (CPG). Such CPGs are neuralmicrocircuits of cells whose synergetic interactions pro-duce multiple states with distinct phase-locked patternsof bursting activity. To study biologically plausible CPGmodels, we develop a suite of computational tools that re-duce the problem of stability and existence of rhythmicpatterns in networks to the bifurcation analysis of fixedpoints and invariant curves of a Poincare return mapsfor phase lags between cells. We explore different func-tional possibilities for motifs involving symmetry breakingand heterogeneity. This is achieved by varying couplingproperties of the synapses between the cells and studyingthe qualitative changes in the structure of the correspond-ing return maps. Our findings provide a systematic basisfor understanding plausible biophysical mechanisms for theregulation of rhythmic patterns generated by various CPGsin the context of motor control such as gait-switching in lo-comotion. Our analysis does not require knowledge of theequations modeling the system and provides a powerfulqualitative approach to studying detailed models of rhyth-mic behavior. Thus, our approach is applicable to a widerange of biological phenomena beyond motor control.

Jeremy WojcikApplied Technology Associates, [email protected]

Robert ClewleyGeorgia State UniversityDepartment of Mathematics and Statistics, [email protected]



MS51

Impact of Single-Neuron Dynamics on Transfer ofCorrelations from Common Input

One source of spike train correlations in the nervous sys-tem is common input, a consequence of the ubiquity ofcoding by populations. The details of how input corre-lations map onto output spike correlations is surprisinglycomplex, depending on single-neuron dynamics in subtleways. Much progress has been made in untangling this re-lationship in Type I and Type II excitable neurons, in bothsimplified phase oscillator and conductance-based models.In this talk, we apply these techniques to novel patterns ofexcitability that arise in the presence of calcium currents.

Andrea K. BarreiroDepartment of MathematicsSouthern Methodist University

154 DS15 Abstracts

[email protected]

MS51

Integrate-and-Fire Model of Insect Olfaction

When a locust detects an odor, the stimulus triggers a se-ries of synchronous oscillations of the neurons in the anten-nal lobe, followed by slow dynamical modulation of the fir-ing rates. I model this behavior using an Integrate-and-Fireneuronal network with excitatory and inhibitory neurons,each with a fast and slow inhibitory conductance response.I derived a coarse-grained model for each (excitatory andinhibitory) neuronal population, which allows for more de-tailed analysis of the olfaction mechanisms.

Pamela B. FullerRensselaer Polytechnic [email protected]

Gregor KovacicRensselaer Polytechnic InstDept of Mathematical [email protected]


MS51

A Network of Excitatory and Inhibitory Neuronswith Gap Junctions

Brain networks are known to give rise to global oscilla-tions that are linked to synchronized neuronal activity.How these oscillations arise is not yet completely under-stood. Researchers believe that electric coupling throughsites called gap junctions may facilitate their emergence,and determine some of their properties. Following datafrom experimental papers, we construct a detailed modelwith synaptic and electric coupling for excitatory and in-hibitory neurons using a modified version of the HodgkinHuxley equations.

Jennifer KileRensselaer Polytechnic [email protected]



MS51

Phase Delayed Inhibition and the Representationof Whisker Deflection Velocity in the Rodent Bar-rel Cortex

The primary sensory feature represented within the rodentbarrel cortex is the velocity with which a whisker has beendeflected. Whisker deflection velocity is encoded within thethalamus via population synchrony (higher deflection ve-locities entail greater thalamic synchrony). Thalamic (TC)

cells project to regular spiking (RS) cells within the bar-rel cortex, as well as to inhibitory cortical fast-spiking (FS)neurons, which in turn project to RS cells. Thus, TC spikesresult in EPSPs followed, with a small time lag, by IPSPswithin an RS cell; i.e., the RS cell decodes TC popula-tion synchrony by employing a phase-delayed inhibitionsynchrony detection scheme. In this work, we constructa biophysical model of a basic ‘building block’ of barrelcortex (the feedforward circuit consisting of TC cells, FScells, and a single RS cell) and we examine the role of thepurely feedforward circuit, and of the phase-delayed inhibi-tion network architecture, in explaining the experimentaldata.

Mainak PatelCollege of William and [email protected]

Runjing LiuDuke [email protected]

Badal JoshiCalifornia State University, San [email protected]

MS52

Extending the Zero Derivative Principle

The Zero Derivative Principle determines an approximateinvariant manifold in a singular perturbation systems ofODEs by repeated differentiation of the slow componentsof the vector field. We show that even if the slow compo-nents are not identified correctly, an approximate invariantmanifold still results from the algorithm, a most useful fea-ture for systems with no explicit time scale separation. Weshow results for the Templator, a simple model for a self-replicating biological system.

Morten BronsTechnical University [email protected]

Eric BenotUniversite de la [email protected]

Mathieu Desroches, Maciej KrupaINRIA [email protected], [email protected]

MS52

Idealized Models for Vortex Shedding and Fluid-Body Interactions

The dynamics of free solid bodies in fluids can be in-fluenced significantly by vortex shedding. Although thisphenomenon depends fundamentally on fluid viscosity,reduced-order models for vortex shedding can be realizedin some cases by imposing velocity constraints on systemsinvolving inviscid fluids. Models obtained in this way canbe framed naturally in the context of geometric mechan-ics and can simplify problems of analysis and control de-sign pertaining to the locomotion of biologically inspiredaquatic robots.

Scott D. KellyMechanical Engineering and Engineering ScienceUniversity of North Carolina at Charlotte

DS15 Abstracts 155

[email protected]

MS52

Visualization of Reduced Granular Dynamics

Reduced dynamical models often lend themselves tostraightforward plots of the correspond dynamics. Yet, theintricate geometry and topology of the resulting phase por-trait can prove challenging to convey in a picture. In thistalk, some recent and ongoing work on the visualization oflow-dimensional dynamical systems will be discussed. Inparticular, results obtained for a reduced model of granu-lar dynamics will be considered. Joint work with D. Black-more and A. Rosato.

Xavier M. TricochePurdue UniversityWest Lafayette, IN [email protected]

MS52

A Novel Semidiscete Scheme for a Reduced Con-tinuum Flow Model

We focus on numerical methods for solving the BSR equa-tions - a reduced dynamical model for granular and otherflows. Using a reliable numerical scheme for the BSRmodel, we study the dynamics of a vertically tapped col-umn of particles. A novel semi-discrete numerical schemehas been derived to demonstrate the value of BSR modelsfor predicting the evolution of granular and other flows.Simulation results are compared with experiments andDEM results.

Hao WuNew Jersey Institute of TechnologyNewark, NJ 07102 [email protected]

Denis BlackmoreNew Jersey Institute of TechnologyNewark, NJ 07102, [email protected]

MS53

Initiation of Rain and Inertial Particles


Markus AbelUniversity of [email protected]

MS53

Aggregate Growth in Optimizing Steel Production


Nikolas RimbertUniversite de Lorraine

[email protected]

MS53

Ostwald Ripening and Nanoparticle Growth


Martin RohloffMPI Dynamics and Self-Organization [email protected]

MS53

Episodic Precipitaton


Jurgen VollmerMax Planck Institute for Dynamics and [email protected]

MS54

Model Free Tuning of Wind Farms for MaximizingPower Production

In this minisymposium, we introduce our recent result onthe model-free approach for maximizing power produc-tion of wind farms. In particular, by exploiting the spe-cial structure of the wind farm about turbines locationand wind direction, we show our multi-resolution SPSAbased method that can achieve fast model-free controllertuning. Simulation results illustrate that the proposedmethod yields the maximum total power production withfaster convergence compared with other existing model-freemethods.

Mohd Ashraf AhmadDepartment of Systems Science,Graduate School of Informatics, Kyoto [email protected]

Shun-Ichi AzumaKyoto [email protected]

Toshiharu SugieDepartment of Systems ScienceKyoto [email protected]

MS54

Basin Stability for Evaluating Large Perturbationsin Power Grids

The human brain, power grids etc. are all characterized bymultistability. We claim that the traditional linearization-based approach to stability is often too local to adequatelyassess how stable a state is. Instead, we quantify it in termsof basin stability, a new measure related to the volume ofthe basin of attraction which is non-local and easily ap-plicable, even to high-dimensional systems and apply it tothe Northern European power system.

Juergen KurthsHumboldt Univ,Germany, Potsdam Institute for ClimateImpactResearch, Germany, and Aberdeen University, UK

156 DS15 Abstracts

[email protected]

MS54

Predicting Critical Links in Complex Supply Net-works

Link failures repeatedly induce large-scale outages in powergrids and other complex supply networks. Yet, which linksare particularly sensitive to inducing such outages is stillnot fully understood. Here we propose two criteria to pre-dict critical links on the basis of the topology of the un-damaged network and its load distribution prior to linkfailure. These criteria outperform critical link predictionbased on pure loads or flows more than six-fold.

Marc TimmeNetwork Dynamics, Max Planck Inst. f. Dyn. & Self-Org.Goettingen, [email protected]

Dirk WitthautSystemforschung und Technologische Entwicklung(IEK-STE)Forschungszentrum [email protected]

Martin RohdenJacobs University [email protected]

Xiaozhu Zhang, Sarah HallerbergNetwork Dynamics, Max Planck Inst. Dynamics [email protected], [email protected]

MS55

Compressive Sensing and Dynamic Mode Decom-position

This work explores compression and compressive sensingstrategies for computing the dynamic mode decomposition(DMD) from heavily subsampled or output-projected data.We demonstrate this architecture on three model systems.First, we construct a spatial signal from a sparse vector ofFourier coefficients driven by a linear dynamical system.Next, we consider the double gyre flow field, which is amodel for chaotic mixing in the ocean. Finally, we explorethe 2D cylinder at Re=100.

Steven BruntonUniversity of [email protected]

MS55

Improving the Accuracy of Dynamic Mode Decom-position in the Presence of Noise

The usefulness of dynamic mode decomposition (DMD) re-lies on its ability to extract accurate dynamic features fromimperfect, noisy data. By deriving the statistical proper-ties of the DMD algorithm, we demonstrate that sensornoise biases the results of DMD in a predictable manner.We introduce a number of modifications to the DMD algo-rithm that give improved robustness to noisy data, whichare validated on a range of synthetic, numerical and exper-imental data sets.

Scott Dawson, Maziar S. Hemati

Princeton [email protected], [email protected]

Matthew O. WilliamsProgram in Applied and Computational MathematicsPrinceton [email protected]


MS55

Parallel Qr Algorithm for Data-Driven Decomposi-tions, in Particular Dynamic Mode Decomposition

Many fluid flows of engineering applications, although verycomplex in appearance, can be approximated by lower-order models governed by a few modes, able to capture thedominant behavior (dynamics) of the system. Recently,different techniques have been developed, designed to ex-tract the most dominant coherent structures from the flow.Some of the more general techniques are based on data-driven decompositions, most of which rely on performing asingular value decomposition (SVD) on a formulated snap-shot matrix. As the number of degrees of freedom of asimulation increases, the resulting data-matrix becomeslonger, otherwise referred to as a tall-and-skinny (TS) ma-trix. Ultimately, the SVD of a TS data-matrix can nolonger be handled on a single processor. To overcome thislimitation, the present study employs the parallel TSQRalgorithm of Demmel et al. (2012), which is further usedas a basis of the underlying parallel SVD. This algorithmis shown to scale well on machines with a large number ofprocessors and, therefore, allows the decomposition of verylarge data-sets.

Taraneh Sayadi, Peter SchmidImperial College [email protected], [email protected]

MS55

Using Dynamic Mode Decomposition to ExtractLinear Global Modes from Nonlinear Fluid FlowSolvers

We present a dynamic mode decomposition (DMD) basedtechnique to capture the dominant linear global modes andeigenvalues using snapshots from a nonlinear flow solver.This approach relies on tracking the growth of perturbationfrom the base state with a nonlinear solver. The guidelinesfor the DMD-based analysis to predict stability propertiesof the flow are discussed. Validations are performed againstthe global stability analysis based on the linearized flowsolver and full eigenvalue problem.

Kunihiko TairaFlorida State [email protected]

Aditya NairFlorida State UniversityMechanical [email protected]

Shervin BagheriKTH Mechanics

DS15 Abstracts 157

Linne Flow [email protected]

MS56

Morse Homology on Spaces of Braids

A Morse Homological theory is constructed on spaces ofbraids, allowing us to consider simultaneously distinct pe-riodic solutions of gradient-like scalar ODEs of the form

us = utt − u+ V (t, u, ut)

with possibly different periods simultaneously. This givesinformation on existence of certain solutions but also makesit possible to do computation on Floer Homology by linkingthe (very) infinite dimensional Floer Homology and thefinite dimensional Conley Index of a discretised dynamicalsystem.

Patrick HafkenscheidVU University [email protected]

MS56

Computing Conley-Morse Databases


Shaun HarkerDepartment of MathematicsRutgers [email protected]

MS56

Rigorous Computing in Strongly Indefinite Prob-lems

Floer homology was originally developed in the late 80s byA. Floer to solve the Arnold Conjecture which states thatthe number of periodic solutions of a periodic Hamiltoniansystem is bounded from below by the topological invari-ants of the manifold on which the Hamiltonian system isdefined. In this setting the periodic orbits are the solu-tions of the Euler-Lagrange equations, i.e. critical pointsof a strongly indefinite action functional. Being an infi-nite dimensional version of Morse theory, Floer homologyis defined in terms of (1) the critical points; (2) their rela-tive indices; and (3) the connecting orbits between criticalpoints with relative index one. While Floer homology is apowerful and celebrated theory, there remains an outstand-ing issue: how computable is it? Recent years have wit-nessed the development of exciting rigorous computationalmethods to make Conley-Morse homology computable andapplicable to a broad class of dynamical systems. Nowthe question is: can we do the same with Floer-Morsehomology? In this talk, we introduce some preliminaryresults about rigorous computing in Floer homology, i.e.we present a rigorous computational technique to computecritical points of strongly indefinite functional as well astheir relative indices.

Jean-Philippe LessardUniversite [email protected]

Jan Bouwe Van Den BergVU University [email protected]

Robert VandervorstVU AmsterdamDepartment of [email protected]

Marcio GameiroUniversity of Sao [email protected]

MS56

Reconstructing Functions from Dense Samples


Vidit NandaDepartment of MathematicsUniversity of [email protected]

MS57

Global Invariant Manifolds Unravelling ShilnikovChaos

We analyse the role of two-dimensional global invariantmanifolds in the transition through a chaotic Shilnikovhomoclinic bifurcation in a 3D model for an optically in-jected laser. We compute the respective two-dimensionalglobal manifolds, and their intersection curves with a suit-able sphere, as families of orbit segments with a two-pointboundary-value-problem setup. This allows us to deter-mine how the arrangement of global manifolds changesthrough the bifurcation and how this influences the topo-logical organisation of phase space. In this way, we findthat the stable manifold of the associated saddle-focus is anaccessible set of the stable manifold of a chaotic saddle (theShilnikov chaotic set) that contains countably many peri-odic orbits of saddle type. In intersection with a suitablychosen sphere we find that this stable manifold is an inde-composable continuum consisting of infinitely many closedcurves that are locally a Cantor bundle of arcs.

Pablo AguirreUniversidad Tecnica Federico Santa MaraDepartamento de [email protected]


MS57

The Lorenz System Near the Loss of the FoliationCondition

We consider the onset of hooks in the Poincare return mapof the famous Lorenz system, when the one-dimensionalLorenz map ceases to accurately represent the dynamics.We employ a two-point boundary value problem set-up tocalculate a point of tangency of the two-dimensional unsta-ble manifold W u(Γ) of a periodic orbit Γ with the stablefoliation. This allows us to continue this boundary curvein any of the system parameters.

Jennifer L. CreaserUniversity of [email protected]

158 DS15 Abstracts


MS57

Analytic Proof of Lorenz Attractors in Flows andMaps

In this talk I will give an overview of the recent results re-garding the theoretical proof of the birth of strange Lorenzattractors in various models. This includes the criteria ofthe birth of Lorenz attractors from global bifurcations offlows (double homoclinic loop), which were also appliedto prove analytically (without a computer assistance) thatsuch an attractor is present in the Lorenz model (the 14thSmale’s problem). This result allows to obtain conditionsof the birth of Lorenz attractors in local bifurcations offlows as well as local and global bifurcations of diffeomor-phisms.

Ivan OvsyannikovUniversity of Bremen, [email protected]

MS57

The Many Facets of Chaos

There are many ways that a person can encounter chaos,such as through a time series from a lab experiment, abasin of attraction with fractal boundaries, a map with acrossing of stable and unstable manifolds, a fractal attrac-tor, or in a system for which uncertainty doubles after sometime period. These encounters appear so diverse, but thechaos is the same in all of the underlying systems; it isjust observed in different ways. We describe these differ-ent types of chaos. We will give two conjectures about thetypes of dynamical behavior that is observable if one ran-domly picks out a dynamical system without searching fora specific property. In particular, we conjecture that frompicking a system at random, one observes (1) only threetypes of basic invariant sets: periodic orbits, quasiperiodicorbits, and chaotic sets; and (2) that all the definitions ofchaos are in agreement.

Evelyn SanderGeorge Mason [email protected]

MS58

The Quantification of the Nonergodic Property ViaSnapshot Attractors: An Application to a Concep-tual Climate Model

The natural measure of a snapshot attractor can be approx-imated only with the use of an ensemble of trajectories. Wequantitatively describe the limitations for extracting esti-mates on the relevant probabilities from the time evolu-tion of a single trajectory. For instance, temporal averagesover finite time intervals taken along a single trajectory arefound to typically differ from the corresponding ensembleaverages. This can be regarded as a measure of the non-ergodic property. In addition, we introduce further, prob-abilistic measures for nonergodicity. We show that evenin stationary systems ergodic behavior sets in for asym-totically long times, no characteristic time exists for theconvergence. Ergodicity is typically broken down even forasymtotically long times in nonautonomous systems with

a permanent shift of their parameters. We illustrate viaa conceptual climate model that this nonergodic snapshotframework might be useful in Earth System dynamics.

Gabor DrotosEotvos [email protected]

Tamas BodaiMeteorologisches InstitutUniversitat [email protected]

Tamas TelEotvos Lorand University, Budapest, HungaryInstitute for Theoretical [email protected]

MS58

Random Attractors and How They Help Under-stand Climate Change and Variability

Until recently, there were two basic approaches to appre-hend the complexity of climate change: deterministicallynonlinear and stochastically linear, or the Lorenz and theHasselmann approach. The theory of random dynami-cal systems provides a framework for unifying these twoapproaches. We apply this theory to study the randomattractors of nonlinear, stochastically perturbed climatemodels, and define climate sensitivity via Wasserstein dis-tances between such attractors. Numerical results are pre-sented for a highly simplified ENSO model.

Michael GhilEcole Normale Superieure, Paris, andUniversity of California, Los [email protected]

MS58

Snapshot Attractors and the Transition to Exten-sive Chaos in Large Systems of Mean-Field Cou-pled Oscillators

We consider systems of many (N) mean-field coupled oscil-lators with two types of dynamics: low dimensional attrac-tors (in which the oscillator states all clump into just a fewvalues), and extensively chaotic states (in which the attrac-tor dimension scales linearly with N). We use the conceptof snapshot attractors to analyze extensively chaotic statesfocusing on the associated fractal dimension. We also studydynamical transitions from low dimensional attractors toextensive chaos and vice verse.

Edward OttUniversity of MarylandInst. for Research in Electronics and Applied [email protected]

Wai Lim KuUniv. of [email protected]

Michelle GirvanUniversity of [email protected]

MS58

SRB Measures for Time-Dependent and Random

DS15 Abstracts 159

Attractors

For autonomous systems of ODEs with chaotic attractors,large-time orbit distributions are described by SRB mea-sures. This theory carries over very well to random dynam-ical systems, for which the picture is in fact simpler due tothe averaging effects of random noise. Some of the ideasextend even to time-dependent attractors without any no-tion of stationary. I will review known ideas and report onnew results.

Lai-Sang YoungCourant Institute of Mathematical SciencesNew York [email protected]

MS59

Chimeras in Networks of Identically Coupled Me-chanical Oscillators

Synchronization has been vastly observed in nature as wellas in man-made systems. Synchronous states are possi-ble when two or more oscillators are interacting with eachother. In particular, arrays of identical oscillators can ex-hibit a fascinating spatiotemporal pattern, termed chimerastate, in which synchronous domains coexist with inco-herent ones. Previous studies have addressed this phe-nomenon theoretically and experimentally. However, thespontaneous emergence of chimeras in translationally in-variant networks remains an experimental challenge. Here,we use a one-dimensional network of identically coupledidentical mechanical oscillators, to implement an experi-mental demonstration yielding this unique phenomenon.Our findings, supported by a mathematical model, bringnew insights into the search for chimeras in nature.

Rosangela FollmannPolytechnic School of University of Sao [email protected]

Daniel Abrams, Adilson E. MotterNorthwestern [email protected], [email protected]

MS59

Synchronization Properties Related to Neighbor-hood Similarity in a Complex Network of Non-Identical Oscillators

We explore in this article complex networks of non-identicalinteracting oscillators. More specifically, the impact ofSimilar or Dissimilar neighborhoods over the emergenceof synchronization is studied. These scenarios are definedbased on a vertex weighted graph measure, the Total Disso-nance, which comprises the sum of the dissonances betweenall neighbor oscillators in the network. Our numerical sim-ulations show that the more homogeneous is a network,the higher tend to be both the coupling strength requiredto phase-lock and the associated final phase configurationspread over the circle. On the other hand, the initial spreadof partial synchronization occurs faster for Similar neigh-borhoods in comparison to Dissimilar ones.

Elbert E. MacauINPE - Brazilian National Institute for Space ResearchLAC - Laboratory for Computing and [email protected]

Celso Bernardo FreitasInstituto Nacional de Pesquisas Espaciais - INPESao Jose dos Campos, SP, [email protected]


MS59

Chimera States in Networks with Symmetry-Breaking Coupling

In a network of Stuart-Landau oscillators with nonlocaltopology and symmetry-breaking coupling we establishnovel partially coherent inhomogeneous spatial patterns,which combine the features of chimera states (coexistingincongruous coherent and incoherent domains) and oscilla-tion death (oscillation suppression), which we call chimeradeath. Moreover, we find chimera states with respectto amplitude dynamics rather than the phase (amplitudechimeras). Additionally, we show that two distinct scenar-ios from oscillatory behavior to a stationary state regimeare possible: a transition from an amplitude chimera tochimera death via in-phase synchronized oscillations, anda direct abrupt transition for larger coupling strength. Webelieve our results are of particular importance for the lifesciences. For instance, these peculiar hybrid states mayaccount for the observation of partial synchrony in neuralactivity, like unihemispheric sleep etc. A. Zakharova, M.Kapeller, E. Scholl, Chimera Death: Symmetry Breakingin Dynamical Networks, Phys. Rev. Lett. 112, 154101(2014)

Anna ZakharovaInstitute of Theoretical PhysicsBerlin, [email protected]

Marie KapellerBerlin Institute of TechnologyBerlin, [email protected]

Eckehard SchollTechnische Universitat BerlinInstitut fur Theoretische [email protected]

MS59

Dynamics of Clustering in Networks with Repul-sive Interaction

In dynamics of simple coupled systems attracting interac-tion usually leads to synchronization. In contrast, repulsiveinteraction is able to split the ensemble into clusters, tocreate multistability and, as we will show, in certain caseseven generate continuous families of oscillatory states.

Michael A. ZaksDepartment of Stochastic Processes, Institute of PhysicsHumboldt University of [email protected]

MS60

Dynamic Mode Decomposition for Multi-

160 DS15 Abstracts

Resolution Analysis

The dynamic mode decomposition (DMD) is an idealmethod for decomposing complex systems into spatio-temporal modes with prescribed temporal signatures. Thefrequency and duration of the data collection process canbe adapted, much as in wavelet theory, to sift out infor-mation at different temporal scales. Indeed, an iterativerefinement of progressively shorter snapshot sampling win-dows and recursive extraction of DMD modes from slow-to increasingly-fast time scales allows for a multi-resolutionDMD analysis that allows for improved analytics. More-over, it also allows for improved analytic predictions of theshort-time future state of the system which is of criticalimportance for control protocols.

J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]

MS60

Approximating the Koopman Operator Using Ex-tended Dynamic Mode Decomposition

It has recently been observed that eigenvalues and modesof the Koopman operator may be approximated using adata-driven algorithm called Dynamic Mode Decomposi-tion (DMD). We first provide a new definition of DMD thatis equivalent to the original, but is more amenable to anal-ysis. We then describe an Extended DMD method whichapproximates the Koopman operator directly, using a user-specified set of basis functions, and allows one to computeKoopman eigenvalues, modes, and eigenfunctions.



MS60

Koopman Operator Techniques in Power GridAnalysis

Spectral properties of the so-called Koopman operator pro-vide an alternative framework for dynamical systems anal-ysis. This enables a new technique of nonlinear modal de-composition, which is referred to as the Koopman ModeDecomposition (KMD). In this presentation, we will out-line our recent efforts on applications of KMD to analysis ofpower grid dynamic performances such as stability analysisand network partitioning. This will lead to a data-drivenframework of analysis and operation of the future powergrid that can handle high penetration of renewable energyresources.

Yoshihiko SusukiKyoto University / [email protected]

MS60

Machine Learning and the Koopman Operator: Al-

gorithms and Applications

We present two extensions of Extended Dynamic Mode De-composition (EDMD), which is a data-driven method thatapproximates the eigenvalues, eigenfunctions, and modesof the Koopman operator. The first is algorithmic: weshow that EDMD can be rewritten as a kernel method,which enables Koopman-based computation in large sys-tems to be performed. The second is an application: theKoopman eigenfunctions are used as a set of intrinsic coor-dinates that enable data-fusion/state-reconstruction tasksto be accomplished.


MS61

What Is the Right Functional for Variational DataAssimilation?

Variational data assimilation refers to matching model tra-jectories with observations. This is usually accomplishedby minimising a quadratic error functional which, in dis-crete time with gaussian perturbations, can be interpretedas the likelihood of a trajectory. Different ways to solvethis problem though can lead to different solutions in thelimit of Δt → 0. This corresponds to the fact that in con-tinuous time, there are several contenders for the likelihoodof a trajectory.

Jochen BrockerUniversity of Reading, UKSchool of Mathematical and Physical [email protected]

MS61

Time Delay Methods for Variational Data Assimi-lation

We investigate an extension to variational data assimilationby modifying the minimized cost function. A penalty to thecost function is added if the state vector at a given time isinconsistent with the measurements at a later time. Theidea is to inform the choice of unmeasured state variablesby looking at how they affect the observed dynamics over awindow of time, rather than comparing the optimum pathonly at adjacent times.

Uriel I. [email protected]

MS61

Filtering Unstable Quadratic Dissipative Systems

The long-time behavior of filters for partially observedquadratic dissipative dynamical systems is considered. It isproven that for both discrete-time and continuous-time ob-servations the 3DVAR filter can recover the signal within aneighborhood defined by the size of the observational noise,as long as a sufficiently large proportion of the state vec-tor is observed; an explicit form for a sufficient constantobservation operator is given. Three models of interest fitinto this class – Lorenz ’63, Lorenz ’96, and 2D Navier-Stokes on a torus. Furthermore, in the case of Lorenz’96, non-constant adaptive observation operators are stud-ied numerically, with data incorporated by use of both the

DS15 Abstracts 161

3DVAR and the extended Kalman filter. It is shown thatfor carefully chosen adaptive observations, the proportionof state coordinates necessary to accurately track the sig-nal is significantly smaller than the proportion proved tobe sufficient for constant observation operator. Indeed it isshown that the necessary number of observations may evenbe significantly smaller than the total number of positiveLyapunov exponents of the underlying system.

Kody LawSRI UQ Center, CEMSE, [email protected]

Abhishek [email protected]

Daniel Sanz-AlonsoUniversity of [email protected]

Andrew StuartMathematics Institute,University of [email protected]

MS61

Observability of Chaotic Lorenz-96 Systems

In 1996 E. Lorenz proposed a ring of one-dimensionalODEs for describing some meteorological quantity atequidistant locations along a latitude circle. Since thenthis systems became a frequently used hyperchaotic modelfor exploring new concepts in dynamical systems theory.In our contribution we shall use it as a prototypical ex-ample for illustrating, testing, and comparing methods forobservability analysis, and state and parameter estimation.

Jan Schumann-BischoffMax Planck Institute for Dynamics and [email protected]

Stefan Luther, Ulrich ParlitzMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected], [email protected]

MS62

Control of Complex Diffusion in Networks ofNEMS

Recent advances in NEMS enable us to explore nonlinearphenomena on networks in unprecedented ways. We applymethods from control of complex diffusion to the oscilla-tors’ complex envelopes as coupled via a linear diffusionterm. We focus on network synchronization and our abilityto guide the system to synchronized states by controllinga small number of oscillators’ natural linear frequencies.Additionally, we investigate control of other limit cycles insmall systems with simple network structure.

Jeff EmenheiserUC DavisPhysics [email protected]

Mehran Mesbahi


Raissa D’SouzaUC [email protected]

MS62

Intrinsic Computation in NEMS

The ways in which nanoscale systems generate, store, andprocess information and dissipate energy yield insights intotheir behavior, potential technological functions, and fun-damental physics of computation. Nanoelectromechanicalsystems (NEMS) are nonlinear and subject to thermal fluc-tuations, making them an ideal experimental platform toprobe the trade-offs between intrinsic computation and en-ergy use. I will present results quantifying intrinsic com-putation in the dynamics of the theoretical counterpart ofmany NEMS devices, the noisy Duffing oscillator.

Russell HawkinsUC DavisComplexity Sciences [email protected]

MS62

Phase Synchronization Between Nanoelectrome-chanical Oscillators

Synchronization, the mutual entrainment of limit cycle os-cillators, is a ubiquitous phenomenon both in the physicaland biological sciences. There exist many observation stud-ies of this phenomenon; however, controlled experiments inthis field are scant. In this talk, I will describe an experi-ment in synchronization based on NanoElectroMechanical(NEMS) oscillators. In addition to the ability to measurethe amplitude and phase dynamics of individual nodes, theexperiment demonstrates a large degree of control over theparameters of the system. Both the coherent and stochas-tic dynamics will be discussed.

Matt MathenyCalifornia Institute of [email protected]

MS63

Ensemble Inflation by Shadowing Techniques

The artificial inflation of ensembles is a technique com-mon to ensemble data assimilation whereby the ensemblevariance is increased in order to prevent deviation of theensemble from the truth. Various techniques for inflatingensembles exist in the literature. This talk will discussensemble shadowing and our implementation of shadow-ing techniques as a method of ensemble inflation. We willalso present results from a low order chaotic system thatsupport using shadowing inflation.

Thomas BellskyArizona State [email protected]

Lewis MitchellUniversity of Adelaide

162 DS15 Abstracts

[email protected]

MS63

Ionospheric Weather Forecasting Using the LetkfScheme

We assimilate satellite observations to forecast ionosphericelectron density using the Local Ensemble TransformKalman Filter(LETKF). This assimilation scheme gener-ates forecasts from an ensemble of initial conditions andforms its analysis by computing a unique linear combi-nation of the forecast ensembles at each grid point usingnearby observations. The ionosphere model used is theTIEGCM. Assessments of the LETKF include validationagainst independent data sources as well as skill in esti-mating ionospheric drivers, forecast ensemble uncertainty,and spatially sharp electron density gradients.

Juan DurazoArizona State [email protected]

MS63

Predicting Flow Reversals in a Cfd Simulated Ther-mosyphon Using Data Assimilation

A thermal convection loop is a circular chamber filled withwater, heated on the bottom half and cooled on the tophalf. With sufficiently large forcing of heat, the directionof fluid flow in the loop oscillates chaotically, forming ananalog to the Earths weather. As is the case for state-of-the-art weather models, we only observe the statistics overa small region of state space, making prediction difficult.To overcome this challenge, data assimilation methods,and specifically ensemble methods, use the computationalmodel itself to estimate the uncertainty of the model tooptimally combine these observations into an initial con-dition for predicting the future state. First, we build andverify four distinct DA methods. Then, a computationalfluid dynamics simulation of the loop and a reduced ordermodel are both used by these DA methods to predict flowreversals. The results contribute to a testbed for algorithmdevelopment.

Andrew ReaganUniversity of [email protected]

MS63

An Application of Lagrangian Data Assimilation toKatama Bay, Ma

Lagrangian data assimilation (LaDA) methods directly useobservations of passive drifters in a flow in order to estimatethe underlying currents. We apply the ensemble Kalmanfilter in this context to a model of Katama Bay in Martha’sVineyard, using real drifter observations. We compare theaugmented-vector method of LaDA to so-called pseudo-Lagrangian methods. Finally, we judge the method‘s per-formance using Eulerian data of the bay from the sametime.


Larry PrattWoods Hole Oceanographic Inst.

[email protected]

Irina RypinaWoods Hole Oceanographic [email protected]

MS64

A Mechanism of Spiral Wave Unpinning and ItsImplications for the Treatment of Cardiac Arrhyth-mias with Periodic Far-Field Pacing

Spiral waves pinned to inexcitable regions of tissue posea particular challenge in the effort to control cardiac ar-rhythmias without a strong defibrillating electrical shock.We investigate one particular unpinning mechanism dueto far-field pulses in a two-dimensional model of excitablemedia and determine its potential benefits over alternativelow-energy strategies such as anti-tachycardia pacing. Fur-thermore, we explore how a simple map-based model canpredict success rates for more realistic scenarios involvingperiodic stimuli.

Philip BittihnBiodynamics LabUniversity of California, [email protected]

Anna BehrendMax Planck Institute for Dynamics and Self-OrganizationGottingen, [email protected]

Stefan LutherMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected]

MS64

The Effects of Cardiac Fibroblasts on Wave Propa-gation in Ventricular Tissue: Insights from Numer-ical Studies of Mathematical Models

We study spiral-wave turbulence in partial-differential-equation models for human cardiac tissue, with both my-ocytes and fibroblasts. We obtain results for cells, with onemyocyte coupled to several fibroblasts, and for tissue. Westudy (a) regularly and (b) randomly arranged fibroblasts,systematize their role in modifying the cardiac action po-tential and the propagation of activation waves, and inves-tigate a low-amplitude control scheme for the suppressionof spiral-wave turbulence.

Alok R. NayakIndian Institute of Science, Bangalore, [email protected]

Rahul PanditIndian Institute of Science, [email protected]

MS64

How to Control Spiral Waves Using Weak Signals:A Few Suggestions

In this talk I will describe a few recently developed meth-ods to control dynamics of spiral waves and spatiotemporalchaos in excitable media. Control is achieved by the ap-plication of small amplitude external signals in a fashion

DS15 Abstracts 163

designed to exploit nonlinear properties of excitable sys-tems. Payoffs for the experimental realisation of such ro-bust methods to control spiral dynamics is enormous andcould have several practical applications, potentially in-cluding a device for safe cardiac defibrillation.

S SridharGhent University, [email protected]

MS64

Controlling Spiral Wave Dynamics in CardiacMonolayers Using Far Field Pulses

Waves in two-dimensional excitable media forms patternssuch as target waves and spiral waves. Spiral waves tend toattach to the heterogeneities in the medium and form verystable structures. We study controlling such waves usingfar field electric pulses in two-dimensional layers of culturedcardiac cells. We will discuss resetting and terminatingspiral waves using periodic far field pulses.

Shajahan Thamara KunnathuMax Planck Institute for Dynamics and Self [email protected]

Sebastian BergMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected]

Valentin KrinskyMax Planck Institute for Dynamics and [email protected]

Stefan LutherMax Planck Institute for Dynamics and Self-OrganizationResearch Group Biomedical [email protected]

MS65

Anatomy Induced Drift of Reentrant Waves in Hu-man Atrium

In biophysically and anatomically realistic model of humanatrium, we demonstrate functional effects of atrial anatom-ical structures on reentrant waves spontaneous drift. Spiralwaves drift from thicker to thinner regions, along ridge-likestructures of pectinate muscules (PM) and cristae termi-nalis, anchor to PM-atrial wall junctions or to some loca-tions with no obvious anatomical features. The insight canbe used to improve low-voltage defibrillation protocols, andpredict atrial arrhythmia evolution given a patient specificatrial anatomy.

Irina BiktashevaUniversity of [email protected]

Vadim N. BiktashevCollege of Engineering, Mathematics and PhysicalSciencesUniversity of [email protected]

Sanjay R. KharcheUniversity of [email protected]

Gunnar SeemannKarlsruhe Institute of [email protected]

Henggui ZhangUniversity of [email protected]

MS65

Stabilized Wave Segments in An Excitable Mediumwith a Phase Wave at the Wave Back

We determine analytically the propagation velocity and theshape of stationary propagating wave segments in excitablemedia supporting excitation waves with trigger fronts andphase backs. Relationship between the medium excitabil-ity and the wave segment parameters is described usingthe free boundary approach. This leads to two univer-sal limits, restricting the region of existence of stabilizedwave segments. Comparison of the analytical results withnumerical simulations of the Kessler-Levine model demon-strates their good quantitative agreement.

Eberhard BodenschatzMax Planck Institute for Dynamics & [email protected]

Vladimir ZykovMax Planck Institute for Dynamics and [email protected]

MS65

Use of Delay-Differential Equations in CardiacModels

Period-2 behavior of cardiac electrical responses, referredto as alternans, often leads to more complicated arrhyth-mias. To date, alternans has been generated mathemati-cally from the loss of stability of the period-1 solution incoupled nonlinear ODE/PDE systems. We build on thefact that delays arise naturally in non-instantaneous cel-lular processes and present an alternative approach usingdelay-differential equations (DDEs), which are known topromote complex dynamics. We analyze the dynamicalbehaviors of our DDE system and discuss the implicationsof our findings.

Elizabeth M. Cherry, Ryan ThompsonRochester Institute of TechnologySchool of Mathematical [email protected], [email protected]

MS65

Spiral Wave Activity in a Mixture of Restingand Oscillating Cardiomyocytes: Limitations onBiopacemaker Development

Self-organization of interconnected elements is importantfor development of biopacemakers. Monolayers of pluripo-tent cell-derived cardiomyocytes exhibit spontaneous acti-vation and consist of a heterogeneous network of cells. Asimple stochastic model of cell distributions combined witha Fitzhugh-Nagumo type model highlights the importanceof spatial granularity of spontaneous cells on biopacemakeractivity. Interestingly, spiral wave activity and the desiredsimultaneous activation of the biopacemaker are found in

164 DS15 Abstracts

opposite spectrum of oscillating cell spatial patterns.

Philippe ComtoisInstitute of Biomedical Engineering,Universite de [email protected]

MS66

Traveling Waves in a Laminar Neural Field Modelof Visual Cortex

One of the challenges in the mathematical and computa-tional modeling of primary visual cortex (V1) is develop-ing recurrent networks models that keep track of neuralactivity with respect to both retinotopic and feature-baseddegrees of freedom such as orientation selectivity. This isfurther complicated by the fact that different cortical layershave different response properties. In this talk we present alaminar neural field model consisting of a superficial layerof orientation-selective cells interacting vertically with adeep layer of non-orientation selective cells. We use themodel to analyze the propagation of orientation selectivityacross cortex.

Samuel R. CarrollUniversity of [email protected]

Paul C. BressloffUniversity of UtahDepartment of [email protected]

MS66

A Computational Model of the Influence of Depo-larization Block on Initiation of Seizure-like Activ-ity

Seizure-like activity can be triggered in a network of ex-citatory and inhibitory neurons when excessive excitationis not suppressed by matching inhibition. Recent exper-imental studies report that inhibitory neurons, receivingstrong excitatory drive, were functionally impaired dueto depolarization block prior to propagation of ictal dis-charges. In this talk, we will discuss different types ofdynamics emerging from a network of excitatory and in-hibitory neurons when inhibitory neurons are prone to de-polarization block. We find that the network may reachthe pathological state via saddle-node bifurcation or ho-moclinic bifurcation. Oscillatory activity present in thenetwork allows us to produce tonic to clonic phase transi-tion observed in epileptic brain slices and human patients.We also discuss the effects of network motifs on promot-ing pathological dynamics. The convergent motifs fromexcitatory neurons onto inhibitory neurons, which may beobserved in mossy fiber sprouting, facilitates depolariza-tion block in inhibitory neurons so that the network canenter the pathological state more easily. The mean fieldequation accounting for the network structure allows us tomake predictions about the effects of different type of net-work motifs. The predictions from the mean field modelare verified by simulating a network of conductance-basedneurons.

Duane NykampSchool of MathematicsUniversity of Minnesota

[email protected]

MS66

Finite Size Effects in Networks of Theta Neurons

The dynamics of a large but finite number of coupled spik-ing neurons is not well understood. We analyze finite sizeeffects in a network of synaptically coupled theta neurons.We show how the system can be characterized by a func-tional integral from which finite size effects are calculatedperturbatively. We consider how finite size effects affectthe stability of the asynchronous state of a uniformly cou-pled network. We then discuss the implications for bumpattractors.

Siwei Qiu

NIDDK/[email protected]

Carson C. ChowNational Institutes of [email protected]

MS66

Optimal Decision-Making in a Changing Environ-ment

We derive a continuous stochastic differential equation de-scribing the optimal accumulation of evidence in a chang-ing environment. Our results apply to two choice decisionmaking wherein the underlying truth switches stochasti-cally. Sequential analysis is used to determine the priorprobabilities of finding the truth in one of two states. Pass-ing to the continuum limit and non-dimensionalizing, wefind the evidence accumulation process depends on a singleparameter, information received per mean switch time.

Alan Veliz-CubaUniversity of HoustonRice [email protected]


Kreimir JosicDepartment of Mathematics, University of [email protected]

MS67

Costs and Benefits of Mutational Robustness inRna Viruses

The accumulation of mutations in RNA viruses is thoughtto facilitate rapid adaptation to changes in the environ-ment. However, most mutations have deleterious effects,especially for viruses. Thus, tolerance to mutations shoulddetermine the nature and extent of genetic diversity in thepopulation. I will present a combination of population ge-netics theory, computer simulation, and experimental evo-lution to examine the advantages and disadvantages of tol-erance to mutations, also known as mutational robustness.

Simone BiancoIBM Research

DS15 Abstracts 165

[email protected]

MS67

Evolutionary Dynamics of Mutator Phenotypes inChanging Environments

Stochastic switching is an example of phenotypic bet-hedging, where offspring can express a phenotype differentfrom that of their parents. Even though phenotypic switch-ing is well documented in viruses, yeast, and bacteria, therehas been little exploration of the evolution of these muta-tor phenotypes under spatially and temporally fluctuatingselection pressures. In this talk, I will use a populationgenetic model to explore the interaction of temporal andspatial variation in determining the evolutionary dynam-ics of phenotypic switching. Although the formulation ofthe model is in terms of non-genetic switching, the sameframework can be used to study the evolution of geneticmutation rates under volatility in selection. This studyoffers new insights into how the interplay of spatial andtemporal environmental variability can influence the evo-lution of phenotypic switching rates, mutation rates, orother sources of phenotypic variation.

Oana CarjaUniversity of [email protected]

MS67

The Acceleration of Evolutionary Spread by Long-Range Dispersal

The spreading of evolutionary novelties across populationsis the central element of adaptation. Unless population arewell-mixed (like bacteria in a shaken test tube), the spread-ing dynamics not only depends on fitness differences butalso on the dispersal behavior of the species. Spreadingat a constant speed is generally predicted when disper-sal is sufficiently short-ranged, specifically when the dis-persal kernel falls-off exponentially or faster. However,the case of long-range dispersal is unresolved: While it isclear that even rare long-range jumps can lead to a dras-tic speedup as air-trafficmediated epidemics show it hasbeen difficult to quantify the ensuing stochastic dynami-cal process. Yet, such knowledge is indispensable for apredictive understanding of many spreading processes innatural populations. I present a simple iterative scalingapproximation supported by simulations that accuratelypredicts evolutionary spread which is determined by atradeoff between frequency and potential effectiveness oflong-distance jumps. In contrast to the exponential lawspredicted by deterministic mean- field approximations, weshow that the asymptotic spatial growth is either accordingto a power-law or a stretched exponential, depending on thetails of the dispersal kernel. More importantly, we providea full time-dependent description of the convergence to theasymptotic behavior which can be anomalously slow and isrelevant even for long times. I will discuss to what extendour results might be used to improve the inference of theevolutionary spread based on genealogical trees, which ishowever a largely open problem.

Oskar HallatschekDepartment of PhysicsUC Berkeley

[email protected]

MS67

Thermodynamics and Statistical Mechanics of Vi-ral Evolution

We analyze a simplified model of viral infection and evo-lution using the grand canonical ensemble and formalismsfrom statistical mechanics and thermodynamics to calcu-late the behavior of a macroscopic number of viruses, andto derive thermodynamic variables for the system. Wemodel the infection process as a series of energy barriersdetermined by the genetic states of the virus and host asa function of immune response and system temperature.We find a phase transition between a positive temperatureregime of normal replication and a negative temperaturedisordered phase of the virus. These phases define differ-ent regimes in which different genetic strategies are favored.Perhaps most importantly, it demonstrates that the sys-tem has a real thermodynamic temperature. For normalreplication, this temperature is linearly related to effectivetemperature. For all temperatures and immunities studied,we find a universal curve relating the order parameter toviral evolvability. Real viruses have finite length RNA seg-ments that encode for proteins which determine their fit-ness; hence the methods put forth here could be refined toapply to real biological systems; perhaps providing insightinto immune escape, the emergence of novel pathogens andother results of viral evolution.

Barbara Jones, James KaufmanIBM [email protected], [email protected]

Justin LesslerJohns Hopkins Bloomberg School of Public [email protected]

MS68

Characterizing the Structure of Multilayer Net-works

The development of Complex Network’s Theory is provid-ing radical new ways of understanding many different pro-cesses from physical, social, engineering, information andbiological sciences. Several notions, such as networks ofnetworks, multidimensional networks, multilevel networks,multiplex networks, interacting networks, interdependentnetworks, and many others have been introduced, and evendifferent mathematical approaches, based on tensor repre-sentation have been proposed. In this talk we will discussa general framework for multilayer networks that includesthe great majority of the different approaches addressed sofar in the literature and review some of attempts to ex-tend the notions, measures and models from single layer tomultilayer networks.

Regino CriadoUniversidad Rey Juan [email protected]

Miguel RomanceDepartamento de Matematica AplicadaUniversidad Rey Juan [email protected]

MS68

Synchronization and the problem of Targeting in

166 DS15 Abstracts

Multilayer Networks

We concentrate on the case involving a two-layer master-slave network to steer a desired collective behavior, not nec-essarily synchronous. The problem is here tackled througha Master Stability Function approach, assessing the stabil-ity of the aimed dynamics, and through a selection of nodesto be targeted. We show that the degree of a node is a cru-cial element in this selection process, and that the target-ing mechanism is most effective in heterogeneous scale-freearchitectures.

Ricardo GutierrezDepartment of Chemical PhysicsThe Weizmann Institute of [email protected]

Irene Sendina NadalUniversidad Rey Juan [email protected]

Massimiliano ZaninTechnical University of [email protected]

David PapoUniversidad Politecnica de Madrid, [email protected]

Stefano BoccalettiCNR-Istituto dei Sistemi [email protected]

MS68

Game and Diffusion Dynamics in Multilayer Net-works

Besides the structure of interactions within networks, alsothe interactions between networks are of the outmost im-portance. We therefore study the outcome of the evolution-ary games on multilayer networks that are connected bymeans of a utility function, which determines how payoffson networks jointly influence the success of players in eachindividual network.. To reach this aim, we consider thesymmetric, asymmetric utility function and find the sym-metric breaking phenomenon and the spontaneous emer-gence of multilayer network reciprocity. Along this line, therole of partially correlation is investigated and the optimalcondition for cooperation is found. Finally, we consider theco-evolution mechanisms of evolutionary games on multi-layer networks and find that the optimal cooperation canbe attributed to individual self-organization trait.

Zhen WangBaptist University of Hong [email protected]

MS68

Synchronization in Time Varying Networks: theNon Commutative Case

We provide a rigorous solution to the problem of construct-ing a structural evolution for a network of identical cou-pled dynamical units switching between topologies withoutstructural constraints. Our method guarantees that thecoupling matrices eigenvectors change smoothly in time.This allows to extend the Master Stability Function formal-ism, and to use it to assess the stability of a synchronized

state when the network topology evolution is fully general,and not necessarily restricted to commuting structures.

Charo I. del GenioUniversity of [email protected]

MS69

The Response of Statistical Averages to SmallStochastic Forcing

We present a response theory for statistical averages ofdeterministic dynamical systems perturbed by a smallstochastic forcing. We derive the response formula ex-plicitly in terms long-time averages of the tangent mapof the unperturbed system, and show that the responseis the second-order effect with respect to the magnitudeof perturbation. We also demonstrate that for a finite re-sponse time the response is consistent with the predictionof the classical response theory for stochastic systems withsmooth invariant distribution density perturbed by a smallstochastic forcing.

Rafail AbramovDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at [email protected]

MS69

Is Our Sensing Compressed?

Considering many natural stimuli are sparse, can a sensorysystem evolve to take advantage of sparsity? We show sig-nificant downstream reductions in the numbers of neuronstransmitting stimuli in early sensory pathways might be aconsequence of sparsity. Our work points to a potentialmechanism for transmitting stimuli related to compressed-sensing (CS) data acquisition. Through simulation, we ex-amine the characteristics of networks that optimally en-code sparsity and the role of receptive fields in stimulussampling.


MS69

A Multiscale Method for Optical Responses ofNano Structures

We introduce a new framework for the multiphysicalmodeling and multiscale computation of nano-opticalresponses. The semi-classical theory treats the evolu-tion of the electromagnetic field and the motion of thecharged particles self-consistently by coupling Maxwellequations with Quantum Mechanics. To overcome the nu-merical challenge of solving high dimensional many bodySchrodinger equations involved, we adopt the Time Depen-dent Current Density Functional Theory (TD-CDFT). Inthe regime of linear responses, this leads to a linear sys-tem of equations determining the electromagnetic field aswell as current and electron densities simultaneously. Aself-consistent multiscale method is proposed to deal withthe well separated space scales. Numerical examples arepresented to illustrate the resonant condition.

Di Liu

DS15 Abstracts 167

Michigan State UniversityDepartment of [email protected]

MS69

Parareal Methods for Highly Oscillatory Dynami-cal Systems

We introduce a multiscale parareal method that efficientlynumerically integrates highly oscillatory ordinary differen-tial equations. The algorithm computes a low-cost approx-imation of all slow variables in the system. Then, fastphase-like variables are obtained using the parareal it-erative methodology and an alignment algorithm. Themethod may be used either to enhance the accuracy andrange of applicability of the multiscale method in approx-imating only the slow variables, or to resolve all the statevariables. The numerical scheme does not require that thesystem is split into slow and fast coordinates. Moreover,the dynamics may involve hidden slow variables, for exam-ple, due to resonances. Convergence of the parareal itera-tions is proved and demonstrated in numerical examples.

Richard TsaiDepartment of MathematicsUniversity of Texas, [email protected]

MS70

Invariant Manifolds of Multi Interior Spike Statesfor the Cahn-Hilliard Equation

We construct invariant manifolds of interior multi-spikestates for the nonlinear Cahn-Hilliard equation and theninvestigate the dynamics on it. An equation for the mo-tion of the spikes is derived. It turns out that the dy-namics of interior spikes has a global character and eachspike interacts with all the others and with the boundary.Moreover, we show that the speed of the interior spikesis super slow, which indicates the long time existence ofdynamical multi-spike solutions in both positive and neg-ative time. This result is obtained through the applicationof a companion abstract result concerning the existence oftruly invariant manifolds with boundary when one has onlyapproximately invariant manifolds.

Peter W. BatesMichigan State UniversityDepartment of [email protected]

MS70

Oscillatory Pulses in FitzHugh-Nagumo

It is well known that the FitzHugh-Nagumo system ex-hibits stable, spatially monotone traveling pulses. Also,there is numerical evidence for the existence of spatiallyoscillatory pulses, which would allow for the constructionof multi-pulses. Here we show the existence of oscillatorypulses rigorously, using geometric blow-up techniques andsingular perturbation theory.

Paul A. CarterDepartment of MathematicsBrown [email protected]

Bjorn Sandstede

Division of Applied MathematicsBrown Universitybjorn [email protected]

MS70

Slow-Fast Factorization of the Evans Function Viathe Riccati Transformation in the Semi-StrongRegime

The complexity of singularly perturbed linear stabilityproblems can be reduced by factorizing the Evans functionin accordance with the scale separation. The factoriza-tion has always been established by geometric arguments,customized for the specific equations and solutions underconsideration. We present an alternative method, that for-malizes and generalizes the factorization procedure. Thisanalytic method is based on the Riccati transformation.We employ our techniques to study the spectral stabilityof semi-localized periodic pulse patterns.

Bjorn De RijkLeiden [email protected]


Jens RademacherUniversity of [email protected]

MS70

Travelling Waves for Fully Discretized BistableReaction-Diffusion Problems

We study various temporal and spatial discretization meth-ods for bistable reaction-diffusion problems. The main fo-cus is on the functional differential operators that arise af-ter linearizing around travelling waves in the spatially dis-crete problem and studying how the subsequent discretiza-tion of time affects the spectral properties of these opera-tors. This represents a highly singular perturbation thatwe attempt to understand via a weak-limit method basedon the pioneering work of Bates, Chen and Chmaj (2003).Once this perturbation is understood, one can study theexistence and (non)-uniqueness of waves in the fully dis-cretized reaction-diffusion system.

Hermen Jan HupkesUniversity of LeidenMathematical [email protected]

MS71

Nonlocal Aggregation Models: A Primer of SwarmEquilibria

Biological aggregations (swarms) exhibit morphologies gov-erned by social interactions and responses to environment.Starting from a particle model we derive a nonlocal PDEdescribing evolving population density. We study equilib-ria and their stability via the calculus of variations whichyields analytical solutions. These solutions include featuressuch as spatial localization with compact support, massconcentrations, and discontinuous density jumps that arealso observed numerically. We apply our methods to a

168 DS15 Abstracts

model of locust swarms.

Andrew J. BernoffHarvey Mudd CollegeDepartment of [email protected]

Chad M. TopazMacalester [email protected]

MS71

Fire Ants Build, Morph, and Repair to SurviveFloods

Fire ants are model organisms for studying active self-healing materials. By linking their legs together, theybuild highly interconnected networks that can quickly re-arrange themselves in response to applied stress. In thistalk, we present experiments and modeling that elucidatetheir construction. Spherical rafts of ants morph into pan-cakes within minutes; towers are constructed to provide anequal compressive load on each ant. We also use plate-on-plate rheology to show ants modify their elastic and viscousmoduli by rearrangement of their bodies. Particular con-sideration is given to showing how structural shape andmaterial properties arise from movement and interactionsbetween ants.

David HuGeorgia Institute of [email protected]

MS71

Quantifying Collective Cell Migration During Can-cer Progression

During cancer progression, tumor cells migrate throughoutthe body, forming clinically dangerous secondary tumors.This metastatic process begins when cells leave the primarytumor, either as individual cells or collectively migratinggroups. Using quantitative image analysis techniques, weare able to extract motion information from time-lapse im-ages of epithelial sheets with varying malignancy. Adapt-ing metrics originally used to study fluid flows we char-acterize the dynamics of these cell lines and compare tocollective dynamics models.

Rachel LeeDepartment of PhysicsUniversity of Maryland College [email protected]

Haicen YueUniversity of California San [email protected]

Wouter-Jan RappelDepartment of PhysicsUniversity of California, San [email protected]

Wolfgang LosertDepartment of PhysicsUniversity of Maryland, College Park

[email protected]

MS71

Aggregate Behaviors of Heterogeneous, Delay-Coupled Agents

Emerging collective motions of swarms of interactingagents are a subject of great interest with a wide range ofapplications. We show, using mean-field analysis, how col-lective motion patterns and segregation of populations ofagents with different dynamic properties emerge naturallyin a model based on self-propulsion and attractive pair-wise interactions between delay-coupled agents. We showpersistence of behaviors with non-global coupling and re-duced swarm populations, and verify these results throughsimulation and experiments.

Klementyna SzwaykowskaPlasma Physics DivsionNaval Research [email protected]

Christoffer R. HeckmanU.S. Naval Research [email protected]

Luis Mier-y-TeranJohns Hopkins Bloomberg School of Public [email protected]


MS72

Clustering, Malleability and Synchronization ofHodgkin-Huxley-Type Neurons

In this work we consider a ”network of network” of burst-ing neurons described by the Huber-Braun model. Eachnetwork is coupled internally in a small word scheme whileeach network is coupled to all other networks using theconnectivity matrix of the cat cerebral cortex. Three dy-namical behavior are analyzed: network clustering genera-tion, characterized by the coherence of a group of network;malleability of the entire network face small changes in theintra coupling (internal to a network) and inter coupling(between networks) parameters; and the synchronization ofthe entire network. In particular we pay attention in thecomplex interplay between inter and intra coupling thatmakes the network to be very adaptive to small variationson the coupling parameters.

Sergio R. Lopes, Thiago de L. PradoDepartment of PhysicsFederal University of [email protected], [email protected]


Jose C. P. ConinckDepartment of MathematicsFederal Technological University of [email protected]

DS15 Abstracts 169

Juergen KurthsHumboldt Univ,Germany, Potsdam Institute for ClimateImpactResearch, Germany, and Aberdeen University, [email protected]

MS72

Nontrivial Collective Dynamics in Networks ofPulse Coupled Oscillators

A wealth of complex phenomena arise in coupled phaseoscillators – typically associated to various forms of syn-chronization – but the collective (macroscopic) dynamicsitself is usually regular (either consisting in a fixed pointor in a limit cycle for the macroscopic variables). Thisis somehow surprising, as the collective dynamics followsfrom the evolution of functional, i.e. infinite dimensional,equations. We discuss a few examples, where the collectivemotion is chaotic and possibly even high-dimensional. Dis-order in the form of diversity among the oscillator frequen-cies (such as in the standard Kuramoto model) appearsto be a basic ingredient, accompanied by the selection ofsuitable phase response curves. The possible extension tophase-oscillators setups will be also discussed.

Antonio PolitiInstitute for Complex Systems and Mathematical Biology,University of Aberdeen, [email protected]

Ekkehard UllnerICSMB, Department of PhysicsUniversity of Aberdeen, [email protected]

MS72

Synchronization in a Cortical Multilayered Com-putational Model: A Simulation Study

We performed a simulation study on the emergence of syn-chronous states in a cortical network model. The modelconsists of excitatory and inhibitory neurons arranged infour layers representing local cortical circuit. Neurons aredescribed by Izhikevich model with parameters that repro-duce firing behavior of different excitatory and inhibitoryneuronal types. We studied versions of the model with-out synaptic plasticity and with synaptic plasticity mod-eled by an asymmetric spike-timing-dependent plasticity(STDP) rule. The version without synaptic plasticity dis-played asynchronous irregular spontaneous activity whilethe version with STDP displayed synchronous activity withproperties dependent on the neuronal types comprising thenetwork.

Antonio C. Roque, Renan O. Shimoura, Rodrigo F. O.PenaDepartment of Physics, FFCLRPUniversity of Sao Paulo, Ribeirao Preto, SP, [email protected], [email protected], [email protected]

MS72

Effects of Reciprocal Inhibitory Coupling in Syn-chronous Neurons

The influences of chemical and electrical synapses are in-vestigated here using Hodgkin-Huxley model neurons. Westudy the dynamics displayed by a pair of neurons coupled

by either (i) only chemical inhibition or by (ii) electricalcoupling first and then chemical inhibition. In both scenar-ios the neuron with the lower firing rate stops spiking forstrong enough inhibition, while the faster neuron remainsactive. However, in scenario (ii) the originally slower neu-ron stops spiking earlier, suggesting that synchronizationintroduces an element of instability into the two-neuronnetwork.

Epaminondas RosaIllinois State UniversityDepartment of [email protected]

MS73

Crossover Collisions of Scroll Waves

The interaction of a pair of scroll waves is studied in achemical system by optical tomography. When the two lo-cally counter-rotating filaments approach each other closerthan radius of the spiral core, they may collide. Thesecrossover collisions lead to a rupture and a subsequent re-connection of the filaments. Each reconnected filamentconsisted of parts that originated from both of the originalfilaments. The conditions for rupture and reconnection offilaments will be discussed.

Dennis KupitzInstitut of Experimental [email protected]

Marcus HauserInstitute of Experimental PhysicsOtto-von-Guericke-University, Magdeburg, [email protected]

MS73

Role of Small Sized Heterogeneities in the Onsetand Perpetuation of Arrhythmias

We investigate, in silico, the dynamics of rotors in 2D andin an anatomical model of human ventricles. We study theeffect of small size ionic heterogeneities, similar to thosemeasured experimentally. We show that they can anchorand also attract rotors rotating at a substantial distancefrom the heterogeneity. It depends on the extent of theheterogeneities and can be as large as 5-6 cm. We discusspossible mechanism of the observed phenomena.

Alexander PanfilovDepartment of Physics and Astronomy, Gent [email protected]

Arne Defauw, Nele VandersickelDepartment of Physics and Astronomy GhentUniversity,[email protected], [email protected]

Peter DawyndtDepartment of Applied Mathematics, Computer ScienceandStatistics, Ghent University, [email protected]

MS73

Effects of Substrate Geometry on Spiral Wave Chi-

170 DS15 Abstracts

rality

We introduced inexcitable obstacles into 1-cm-diametercardiac monolayers, leading to the initiation of clockwise-rotating, counterclockwise-rotating, and pairs of spiralwaves. Simulations demonstrated that the location of theobstacle and the side pacemaker frequency controlled spi-ral wave chirality. Instabilities observed in action potentialduration restitution curves computed at different spatiallocations predicted sites of propagation failure, and, thus,spiral wave chirality.

Thomas D. QuailMcGill [email protected]

Alvin Shrier, Leon GlassMcGill UniversityDepartment of [email protected], [email protected]

MS73

Scroll Waves in Viscous Systems with Stokes Flow:Writing Filaments and Other New Tricks

Excitable and oscillatory reaction-diffusion systems canself-organize vortex states that rotate around one-dimensional phase singularities. We have studied the dy-namics of these scroll waves and filaments in the Belousov-Zhabotinsky reaction with a particular emphasis on theinteraction of filaments with internal heterogeneities andthe system boundaries. For a highly viscous system, scrollwaves can be pinned to moving glass rods and repositionedat will. If the glass rod extends only along a fraction ofthe filament, the free filament gets stretched out along therod trajectory and the trailing end moves with a speedthat depends on the local curvature. We also performedexperiments on scroll wave drift along step-shaped heightchanges. Our experimental results are complemented bysimulations of which some explicitly consider the Stokesflow generated by the slowly moving heterogeneities.

Oliver SteinbockDepartment of Chemistry and BiochemistryFlorida State [email protected]

MS74

Dynamics of Networks with Partially SymmetricConnectivity Matrices

According to the long-standing Hebbian hypothesis, exter-nal stimuli are stored in long-term memory thanks to modi-fications of synaptic connectivity in neural circuits that areactivated by such stimuli. However, the details of synaptic‘learning rules’, as well as the impact of synaptic plastic-ity on network dynamics, are still unclear. In this talk,I will describe two complementary directions whose goalis to improve our understanding of these questions. Thefirst consists in investigating the effects of realistic ‘learn-ing rules’ that have been used to fit in vitro data on net-work dynamics. The second consists in inferring synaptic‘learning rules’ from the changes in neuronal activity uponrepeated presentations of initially novel stimuli.

Nicolas BrunelDepartments of Statistics and NeurobiologyThe University of Chicago

[email protected]

MS74

Oscillations in Neuronal Networks

Neurons in the visual cortex exhibit heterogeneity in fea-ture selectivity and the tendency to generate action po-tentials synchronously with other nearby neurons. Visualresponses from cat visual cortex during gamma oscillationsreveal a postive correlation between strength of oscillations,propensity towards synchronization, and sharpness of ori-entation tuning. We present a model that can account forthe correlations between these three properties and couldapply more generally to any brain region with analogousneuron types.

Stefanos FoliasDepartment of Mathematical SciencesUniversity of Alaska [email protected]

MS74

On a Kinetic Fitzhugh-Nagumo Equation

We consider the dynamics of the electric activity of a neu-ron within a large network, described at a mesoscopic scaleincorporating intrinsic stochastic dynamics and disorderedinteractions. We are concerned with showing (i) existenceand linear stability of steady states, as well as (ii) nonlinearexponential stability in the weak connectivity regime. Weillustrate these results analyzing the electrically coupledFitzhugh-Nagumo kinetic equation.

Cristobal QuininaoLaboratoire Jacques-Louis [email protected]

MS74

Assembling Collective Activity in Neural Circuits

Experimental breakthroughs are yielding an unprecedentedview of the brain’s connectivity and of its coherent dynam-ics. But how does the former lead to the latter? We usegraphical and point process methods to reveal the contri-bution of successively more-complex network features tocoherent spiking.

Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected]

MS75

Entropy, Dissipation and Information Processing inModels of Complex Systems

Recent advances in the study of (biological) complex sys-tems have shown an intimate connection between dissi-pation and computation. Information theory provides auniversal framework to formalize these notions. In thistalk, I review complex systems as information-processingdevices, which compute patterns at the expense of infor-mation written to hidden degrees of freedom. As an exam-ple, I review how such a picture yields a direct connectionbetween the notions of dissipation used in the major mod-elling paradigms of complex systems: Markovian stochasticdynamics (stochastic thermodynamics, Monte-Carlo simu-lations) and thermostatted equations of motion (molecular

DS15 Abstracts 171

dynamics simulations).

Bernhard AltanerMax-Planck Insitute for Dynamics and [email protected]

MS75

Degrees of Information Processing in Chaotic Dy-namical Systems

It is well known that chaotic dynamical systems generateinformation. This is typically captured by the Kolmogorov-Sinai entropy, the supremum of Shannon entropy rates overall possible partitions of the system. We have recentlyshown that this is a rather crude measure, and can in factbe dissected in to two pieces: a part that is rememberedby being correlated with future behavior, and a part whichis forgotten and plays no role in the temporal evolution ofthe system. Here, we show that although the entropy rateis invariant for both Markov and generating partitions ofthe system, its decomposition is not. We compare thesevalues for the tent map, and comment on what this meansfor study of such chaotic systems as information generatorsor processors.

Ryan G. JamesUniversity of California, [email protected]

MS75

Time-Dependent Chaotic Attractors Shape Infor-mation Content in Neural Networks

Large networks of sparsely coupled, excitatory and in-hibitory cells occur throughout the brain. They are re-sponsible for ongoing and complex computations, the ex-act mechanisms of which are poorly understood. Groups ofconnected neurons form very high-dimensional DynamicalSystems that are often responding to rich, temporally fluc-tuating signals from various afferents. For many modelsof these networks, a striking feature is that their dynamicsare chaotic and thus, are sensitive to small perturbations.How does this chaos manifest in the neural code? Under-standing how the dynamics of large driven networks shapetheir capacity to encode and process information presents asizeable challenge. Inspired by this question, I will discussthe use of Random Dynamical Systems Theory as a frame-work to study information processing in high-dimensional,non-autonomous systems. Using a neural network model,I will present recent results linking random strange attrac-tors to noise entropy and input discrimination of dynamicalobservables.

Guillaume LajoieDepartment of Applied MathematicsUniversity of [email protected]

MS75

Deconstructing Maxwells Demon

The thermodynamic role of information processing has be-come an active topic of research because of its relevanceto a wide range of problems, from bacterial sensing andfeedback control of microscopic systems to single-photoncooling of atoms. This is most dramatically captured inthe gedanken experiment of Maxwells demon, where a neat-fingered intelligent being can violate the second law of ther-modynamics by extracting work from a single heat source.

With an exactly solvable model, we discuss a possible work-ing mechanism of the demon. We draw a nonequilibriumphase diagram and show that, depending on the locationon the diagram, the model can act either as an engine, con-verting into work the extracted heat from the single heatsource, or as a Landauer eraser, erasing information andconsuming external work in the process.

Dibyendu MandalUniversity of California, [email protected]

MS76

Microfluidic Networks of Belousov-ZhabotinskyDrops

Several microfluidic based experimental systems of net-works of non-linear chemical oscillators are presented. 2Dplanar arrays of oscillators with nearest neighbor couplinginvolving both inhibitory and excitatory species are devel-oped. We explore phenomena such as synchronization, os-cillator death and assess the number of attractors, as wellas their basin of attraction, as a function of the topologyof the network and the heterogeneity of the oscillators andtheir coupling strength.

Seth FradenBrandeis UniversityDepartment of [email protected]

MS76

Synchronization and Network Topology of Electro-chemical Micro-Oscillators in On-Chip IntegratedFlow Cells

We present that oscillatory reactions taking place on elec-trode arrays in single or branched flow channels inherentlyform a network, whose characteristics can be tuned withthe position of the electrodes. The network structure isdecoded from experimental measurements and the struc-ture is interpreted with a theory. The unusual, spatiallydependent network topology induces a unique dynamicalresponse in the form of a spatial gradient in the extent ofsynchronization with large set of electrodes.

Istvan Z. Kiss, Yanxin Jia, Yifan Liu, Jasmine ColemanDepartment of ChemistrySaint Louis [email protected], [email protected], [email protected],[email protected]

MS76

Synchronization in Networks of Coupled ChemicalOscillators

We have studied heterogeneous populations of chemical os-cillators to characterize different types of synchronizationbehavior. The formation of phase clusters in stirred sus-pensions of Belousov-Zhabotinsky oscillators is described,where the (global) coupling occurs through the medium.We then describe the formation of phase clusters andchimera states in populations of photosensitive oscillators.The nonlocal coupling occurs via illumination intensitythat is dependent on the state of each oscillator. The be-havior of oscillators in ring configurations as a function ofthe number of oscillators is described, including travelingcluster states. References: A. F. Taylor et al., AngewandteChemie Int. Ed. 50, 10161 (2011); M. R. Tinsley et al.,

172 DS15 Abstracts

Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev.Lett. 110, 244102 (2013).

Kenneth ShowalterWest Virginia UniversityDepartment of [email protected]

MS76

Long Transients to Synchronization in RandomNetworks of Electrochemical Oscillators

In sparse, connected, random networks of attractively cou-pled oscillators one can expect a range of dynamical equi-libria, such as complete synchronization, phase synchro-nization, partial synchronization or incoherence [Toenjeset al., Chaos 20, 033108 (2010)]. Here we report on ex-periments studying the transitions to and from a regimeof phase synchronized electrochemical oscillators formingcomplex wave patterns on a small ring network with a fewrandom non-local connections.

Ralf ToenjesPotsdam UniversityDept. of Physics and [email protected]

Michael SebekSaint Louis UniversityDepartment of [email protected]

Istvan Z. KissDepartment of ChemistrySaint Louis [email protected]

MS77

Travelling Waves and Canards in a Model ofWound Healing Angiogenesis

We discuss the existence of travelling waves in a singularlyperturbed model of wound healing angiogenesis. We usegeometric singular perturbation theory, supplemented withcanard theory due to a fold in the critical manifold wherenormal hyperbolicity is lost. Along this fold, canard pointsmay exist that allow solution trajectories to pass throughthe fold. These so-called canard solutions are crucial toestablishing the existence of travelling waves, in particular,that contain shocks.

Kristen HarleyQueensland University of [email protected]


Robert MarangellThe University of [email protected]

Graeme PettetQueensland University of TechnologySchool of Mathematical [email protected]

Martin WechselbergerUniversity of [email protected]

MS77

Singularities in Front Bifurcations with Scale Sep-aration

A paradigm for the occurrence of fronts are phase sepa-ration phenomena and Allen-Cahn type equations providethe simplest model class. The coupling to further equa-tions with scale-separation leads to a surprisingly rich classof singularly perturbed problems that is amenable to anal-ysis. Over the past decades several methods have beendevelopped to obtain rigorous existence and stability re-sults also for more complicated patterns than single fronts.In this talk we showcase an analysis of a three-componentmodel with two linear equations coupled to an Allen-Cahnequation with scale separation. We show the front dynam-ics is organized by a butterfly catastrophe that leads toaccelerating and direction reversing slow fronts. In addi-tion, a more general result concerning the imbedding ofarbitrary singularities in such front bifurcations is shown.This is joint work with Martina Chirilus-Bruckner, Petervan Heijster and Arjen Doelman.


MS77

Pinning and Unpinning in Nonlocal Equations

We investigate pinning regions and unpinning asymptoticsin nonlocal equations. We show that phenomena are re-lated to but different from pinning in discrete and inhomo-geneous media. We establish unpinning asymptotics usinggeometric singular perturbation theory in several examples.We also present numerical evidence for the dependence ofunpinning asymptotics on regularity of the nonlocal con-volution kernel.

Taylor AndersonMount [email protected]

Gregory Faye

Ecole des hautes etudes en sciences [email protected]

Arnd ScheelUniversity of MinnesotaSchool of [email protected]

David StaufferCornell [email protected]

MS77

Canard Supersonique

Looking at the gas dynamics of stars under the assumptionof spherical symmetry, I will show that transonic eventsin such systems are canard phenomena – peculiar solu-tion structures identified in geometric singular perturba-tion problems. Consequently, stellar winds are carried by

DS15 Abstracts 173

supersonic ducks, and canard theory provides a mathe-matical framework for this astrophysical phenomenon. So,whenever you have the chance to watch an aurora, remem-ber the superheros behind that scene – transonic canards!


MS78

Control of Moreau’s Sweeping Process: Some Re-sults and Open Problems

While the existence theory is a very active area of researchsince the ’70s, the understanding of the dynamics and ofthe control of the sweeping process is an entirely new sub-ject. The talk will focus on some models and open prob-lems, together with recent results, obtained in collabora-tion with other authors (including Nguyen D. Hoang, B.Mordukhovich, R. Henrion), on necessary conditions forvarious cases of optimal control for the sweeping process.In particular, the case where the moving set depends oncontrol parameters will be considered and the obtained nec-essary conditions will be illustrated through examples. Iftime permits also a minimum time problem will be ad-dressed.

Giovanni ColomboUniversity [email protected]

MS78

On the Response of Sweeping Processes to Pertur-bation

If x0 is an equilibrium of an autonomous differential equa-tion x = f(x) and det ‖f ′(x0)‖ �= 0, then x0 persists un-der autonomous perturbations and x0 transforms into aT -periodic solution under non-autonomous T -periodic per-turbations. In this paper we discover an analogues struc-tural stability for Moreau sweeping processes of the form−u ∈ NB(u) + f0(u), u ∈ R2, i. e. we consider the sim-plest case where the derivate is taken with respect to theLebesgue measure and where the convex set B of the re-duced system is an immovable unit ball of R2. We showthat an equilibrium ‖u0‖ = 1 persists under periodic per-

turbations, if the projection f : ∂B → R2 of f0 on the tan-gent to the boundary ∂B is nonsingular at u0. Supportedby RFBR grants 14-01-00867, 14-01-92004, 13-01-00347.

Mikhail KamenskiDepartment of Mathematics, Voronezh State UniversityUniversitetskaja pl. 1, Voronezh, 394006, [email protected]

Oleg MakarenkovUniversity of Texas at [email protected]

MS78

Dynamics of Sweeping Processes with Jumps in theDriving Term

For discontinuous driving terms, sweeping processes wereoriginally formulated first for step multifunctions and thenextended to BV moving convex sets. Another naturalprocedure consists in extending the classical continuous

process from absolutely continuous to BV driving termsthrough a continuity method [V. Recupero, A continuitymethod for sweeping processes, J. Differential Equations,2011]. We show that this method leads to a new of no-tion of sweeping process and we compare the two differentdynamics.

Vincenzo RecuperoDepartment of MathematicsPolitecnico di Torino, [email protected]

MS78

Estimation and Control Problems in Systems withMoreau’s Sweeping Process

This talk will address control-theoretic design problems fordynamical systems modeled as variants of Moreau’s sweep-ing process. As a first case, we consider physical systemswhich comprise a time-varying Lipschitz vector field andthe set-valued mapping resulting from a first-oder convexsweeping process. A well-posedness result on existence anduniqueness of solutions for such systems is presented. Theresult is used for designing controllers, and state estima-tors in the context of output regulation problem. An ex-tension of these techniques is used to derive Lyapunov sta-bility conditions and design state estimators for systemsinvolving sweeping processes with proximally regular set-valued mappings. We next consider second order sweepingprocesses which are useful in modeling mechanical systemswith unilateral constraints. The problem of velocity esti-mation is considered using only the position measurements,which becomes nontrivial due to discontinuities in the ve-locity caused by the impacts. A state estimator is proposedwhich has the form of a measure differential inclusion. Itis shown that there exists a unique solution to the pro-posed differential inclusion and that solution converges tothe actual velocity of the system.

Aneel TanwaniDepartment of MathematicsUniversity of Kaiserslautern, [email protected]

MS79

The Dynamics of Vortices and Masses over Surfacesof Revolution

One of the today’s challenges is the formulation of the N-body and N-vortex dynamics on Riemann surfaces. In thistalk we show how the two problems are strongly related oneanother from the point of view of the intrinsic geometryof the surface where thedynamics takes place. Given asurface M of metric g and the distribution of matter S onM, we deduce the dynamics of the masses and some of itsproperties.

Stefanella BoattoDep. de Matematica Aplicada, IMUniversidade Federal de Rio de [email protected]

Gladston DuartePos-Graduao do Instituto de MatematicaUniversidade Federal de Rio de [email protected]

David G. DritschelDepartment of Applied Mathematics

174 DS15 Abstracts

University of St [email protected]

Teresa J. StuchiInstituto de FisicaUniversidade Federal de Rio de [email protected]

Carles SimoDepartamento de Matematica i AnalisiUniversitat de [email protected]

Rodrigo SchaeferDepartament de Matematica Aplicada I [email protected]

MS79

Eulerian Geometric Integration of Fluids for Com-puter Graphics

We present two geometric numerical methods for fluid sim-ulation in computer animation. One is built to enforceKelvin’s theorem in a semi-Lagragian manner, while theother is derived from first principles using a finite dimen-sional approximation of the group of volume-preservingdiffeomorphisms. The two resulting time integrators areshown to exhibit much improved numerical behavior. Timepermitting, we will also discuss extensions to magnetohy-drodynamics and geophysical flows.

Mathieu DesbrunDept. of Computing & Mathematical [email protected]

Dmitry PavlovDepartment of MathematicsImperial [email protected]

Evan S. GawlikStanford [email protected]

Yiying TongComputer Science and EngineeringMichigan State [email protected]

Gemma MasonCMS [email protected]

Eva KansoUniversity of Southern [email protected]

MS79

Poincare-Birkhoff Normal Forms for HamiltonianRelative Equilibria

Consider a cotangent bundle Hamiltonian system witha free, proper and compact Lie symmetry. We presentan iterative algorithm suitable for the application of the

Poincare-Birkhoff normal forms method near a relativeequilibrium on a fixed momentum level set.

Cristina StoicaDepartment of MathematicsWilfrid Laurier [email protected]

MS79

Studies on Dynamics of Vortices on a Flat Torus

In this talk I will present a complete description of thedynamics of two vortices on flat tori. The dynamics is de-termined by a Hamiltonian equation for the evolution ofthe center of vorticity with a Hamiltonian function definedin terms of Jacobi theta functions. We describe the bi-furcation curves obtained under variations of the moduleparameter of the torus. The analysis of the stability forsome special solutions are in progress.

Humberto H. de Barros ViglioniDepartamento de MatematicaUniversidade Federal de [email protected]

MS80

Spiral Pinballs

Spiral waves in excitable media possess both wave-like andparticle-like properties. When resonantly forced, spiralcores drift like particles along straight trajectories. Thesetrajectories may reflect from medium boundaries or fromobstacles within the medium. Interestingly, such reflectionsare almost always non-specular (that is, they have english),and this results in interesting ricochet paths within themedium. Paths may be further complicated if the mediumitself undergoes motion.

Jacob LanghamMathematics InstituteUniversity of [email protected]

Dwight BarkleyUniversity of WarwickMathematics [email protected]

MS80

Drift of Scroll Waves in Thin Layers Caused byThickness Features

A scroll wave in a thin layer of excitable medium is sim-ilar to a spiral wave, but may drift depending on layergeometry. Effects of sharp thickness variations are dis-tinct from filament tension and curvature-induced driftsdescribed earlier. We describe these effects asymptotically,with the layer thickness and its relative variation as smallparameters. Asymptotic predictions agree with numericalsimulations for drift of scrolls along thickness steps, ridges,ditches, and disk-shaped thickness variations.

Irina BiktashevaUniversity of [email protected]

Hans DierckxDepartment of Physics and Astronomy

DS15 Abstracts 175

Ghent [email protected]

Vadim N. BiktashevCollege of Engineering, Mathematics and PhysicalSciencesUniversity of [email protected]

MS80

Tidal Forces Act on Cardiac Filaments

During cardiac arrhythmias, scroll waves of electrical ac-tivation rotate around a filament curve. By treating theanisotropy of cardiac tissue as a curved space, I derivethe laws of motion for filaments in anisotropic reaction-diffusion systems. In addition to the familiar filament twistand curvature terms, intrinsic curvature (Riemann curva-ture terms) also act as tidal forces on the filament.

Hans DierckxDepartment of Physics and AstronomyGhent [email protected]

MS80

Computation of Unstable Solutions of CardiacModels on Static and Evolving Domains

Although typical cardiac models respect global Euclideansymmetries, these symmetries are generally broken bychaotic solutions. A generalized amplitude-phase represen-tation allows “decomposition’ of such chaotic multi-spiralsolutions into tiles, each of which contains a single spiraldescribed by an unstable periodic or relative periodic solu-tion that respects translational and rotational symmetrieslocally. We present a method for computing such solutionson irregular domains with stationary or moving boundariesand discuss their properties.

Christopher MarcotteGeorgia Institute of [email protected]

Roman GrigorievGeorgia Institute of TechnologyCenter for Nonlinear Science & School of [email protected]

MS81

First-Passage Times of Random Walks in ConfinedGeometries


Olivier BenichouUniversite Pierre et Marie [email protected]

MS81

Asymptotic Analysis of Narrow Escape Problemsin Non-Spherical 3D Domains

Narrow escape problems for non-spherical 3D domains withN ≥ 1 boundary traps are considered. We compute anasymptotic expression for the average mean first passagetime (AMFPT) for three-dimensional domains bounded by

a level surface of an orthogonal coordinate system. A two-term asymptotic expansion for the AMFPT is derived foran arbitrary N ; it is compared with COMSOL numeri-cal solutions. Steps are taken towards the derivation ofhigher-order asymptotics and a position-dependent MFPTformula.

Alexei F. CheviakovDepartment of Mathematics and StatisticsUniversity of [email protected]

Daniel GomezUniversity of British [email protected]

MS81

First Passage Times in Biological Self-Assembly

Nucleation and self-assembly in biology usually involve afixed number of constituents aggregating into clusters ofa finite maximal size. Motivated by this scenario, we de-rive the corresponding backward Kolmogorov equation forthe cluster probability distribution and study the distribu-tion of times it takes for a single maximal cluster to becompleted, starting from any initial particle configuration.Surprisingly, we find, both analytically and numerically,that faster detachment can lead to a shorter mean timeto first completion of a maximum-sized cluster. This re-sult is due to the redistribution of trajectory weights uponincreasing the detachment rate so that paths that take ashorter time to complete a cluster become more likely.

Maria D’[email protected]

Tom ChouUCLADepartments of Biomathematics and [email protected]

MS81

Signal Focusing Through Active Transport

The precision of cellular signaling and novel diagnostic de-vices is limited by the counting noise imposed by the ther-mal diffusion of molecules. Many macromolecules and or-ganelles bind to molecular motors and are actively trans-ported. We will show that a random albeit directed de-livery of molecules to within a typical diffusion distanceto the receptor reduces the noise correlation time, therebyimproving sensing precision. The conditions for improvedsensing are compatible with observations in living cells.

Aljaz GodecUniversitat [email protected]

Ralf MetzlerInst for Physics & AstronomyUniversity of [email protected]

MS82

Control of Multiscale Dynamical Systems

New applications in materials, medicine, and computers

176 DS15 Abstracts

are being discovered where the control of events at themolecular and nanoscopic scales is critical to product qual-ity, although the primary manipulation of these events dur-ing processing occurs at macroscopic length scales. Thesesystems motivate the creation of tools for the control ofmultiscale systems that have length scales ranging from theatomistic to the macroscopic. This talk describes a system-atic approach that consists of stochastic parameter sensi-tivity analysis, Bayesian parameter estimation applied toab initio computational chemistry calculations and experi-mental data, model-based experimental design, hypothesismechanism selection, and multistep optimization. The ap-plication of control theory to the analysis and design ofmultiscale simulation codes is also discussed.

Richard D. BraatzMassachusetts Institute of TechnologyDepartment of Chemical [email protected]

MS82

Some Results on the Backward Stability of SingularPerturbation Approximations of Linear and Non-linear Stochastic Control Systems

An important aspect of model reduction of large-scale con-trol systems is the estimation of the approximation erroras a function of the control input. A different question iswhether feedback controls computed from a reduced modelare a reasonable approximation of the optimal control forthe original model, the computation of which is often infea-sible. In this talk we present recent results on the backwardstability of singular perturbation approximations of a cer-tain class of stochastic control systems and discuss variousapplications.

Carsten HartmannFreie Universitat Berlin (Free University of Berlin)[email protected]

MS82

Variational Integrators for Multiscale Dynamics

In this talk variational integrators are developed for thestructure-preserving integration of systems with dynamicson multiple time scales. The construction is based on aderivation in closed form via a discrete variational prin-ciple on a time grid consisting of macro and micro timenodes. The structure preserving properties as well as theconvergence behavior of the multirate integrator are ana-lyzed and its performance is demonstrated by numericalexamples.

Sina Ober-BloebaumUniversitat Paderborn (University of Paderborn)[email protected]

Sigrid LeyendeckerUniversity of [email protected]

MS82

Control of Oscillators, Temporal Homogenization,and Energy Harvest by Super-Parametric Reso-nance

We show how to control an oscillator by periodically per-turbing its stiffness, such that its amplitude follows an arbi-

trary positive smooth function. This also motivates the de-sign of circuits that harvest energies contained in infinitesi-mal oscillations of ambient electromagnetic fields. To over-come a key obstacle, which is to compensate the dissipa-tive effects due to finite resistances, we propose a theorythat quantifies how small/fast periodic perturbations affectmultidimensional systems. This results in the discovery ofa mechanism that reduces the resistance threshold neededfor energy extraction, based on coupling a large number ofRLC circuits.

Molei TaoCourant Institute, [email protected]

MS83

Nonlinear Waves in Microsphere-Based Metamate-rials

Locally-resonant metamaterials and granular media areboth highly dispersive and known to drastically affectacoustic wave propagation. In this work, we considerthe nonlinear dynamics of a system at the intersection ofthese two types of media: a locally-resonant metamaterialcomposed of microscale spheres adhesively coupled to anelastic substrate, where the spheres act as nonlinear localresonators. Dynamical simulations of a discrete elementmodel representing the metamaterial are compared withphotoacoustic experimental measurements.

Nicholas BoechlerUniversity of WashingtonDepartment of Mechanical [email protected]

MS83

Multiscale Analysis of Strongly Localized Waves


Guillaume JamesLaboratoire Jean Kuntzmann, Universite de Grenobleand CNRSINRIA [email protected]

MS83

Standing Waves on Tadpole Graphs

We develop a detailed rigorous analysis of edge bifurcationsof standing waves in the nonlinear Schrodinger (NLS) equa-tion on a tadpole graph (a ring attached to a semi-infiniteline subject to the Kirchhoff boundary conditions at thejunction). It is shown in the recent work of C. Cacciapuoti,D. Finco, and D. Noja by using explicit Jacobi elliptic func-tions that the cubic NLS equation on a tadpole graph ad-mits a rich structure of standing waves. Among these, thereare different branches of localized states bifurcating fromthe edge of essential spectrum of an associated Schrodingeroperator. In this work, joint with D. Noja (Milan), we showby using the Lyapunov-Schmidt reduction that the bifurca-tion phenomenon is general for other power nonlinearitiesand moreover, the local properties of bifurcating standingwaves can be characterized in full details. We distinguisha primary branch of never vanishing standing waves bifur-cating from the trivial solution and an infinite sequence ofhigher branches with oscillating behavior in the ring. Thehigher branches are not small at threshold and bifurcate

DS15 Abstracts 177

from the branches of degenerate standing waves with van-ishing tail outside the ring. Each higher nontrivial branchbreaks the symmetry of the degenerate branch. Moreover,we analyze stability of bifurcating standing waves. Namely,we show that the primary branch is composed by orbitallystable standing waves, while the nontrivial higher branchesare linearly unstable near the bifurcation point. The sta-bility character of the degenerate branches remains incon-clusive at the analytical level, whereas heuristic argumentsand numerical approximations support the conjecture oftheir linear instability at least near the bifurcation point.

Dmitry PelinovskyMcMaster UniversityDepartment of [email protected]

MS83

Granular Acoustic Switches and Logic Elements

We present analytical, numerical, and experimentaldemonstration of an acoustic switch, analogous to its elec-tric/optical counterpart, based on a 1D chain of granularcrystals. This system controls the propagation of primaryoutput stress waves by applying secondary control waves,exploiting the nonlinear dynamic effects of the granularchain. We also realize OR and AND acoustic logic gatesusing multiple control signals.

Jinkyu Yang, Feng LiUniversity of [email protected], [email protected]

Paul AnzelCalifornia Institute of [email protected]


Chiara DaraioETH Zurich, Switzerland and California Institute of [email protected]

MS84

Modulating Synaptic Plasticity Within In VitroHippocampal Networks

Synaptic plasticity, in the form of long-term potentiation(LTP) and long-term depression (LTD), is thought to un-derlie learning and memory. Both must be highly regulatedfor proper memory storage to take place. We chemicallyinduce LTP and LTD within networks of hippocampal neu-rons and quantify the changes in action potential firingwithin the purview of network dynamics.

Rhonda DzakpasuGeorgetown UniversityDepartment of [email protected]

MS84

Traveling Patterns in Lateral Inhibition NeuralNetworks

We investigate the necessary condition- asymmetry in thecoupling function, for traveling pulses to exist in a neural

network coupled with lateral inhibition. We then computethe traveling pulses using a system of equivalent delayeddifferential equations derived from the neural field model.We further study the dynamical dependency of travelingpulses on the gain and coupling parameters, and demon-strate how to determine the stability of given travelingpulses.

Yixin GuoDrexel UniversityDepartment of [email protected]

Aijun ZhangDepartment of MathematicsDrexel [email protected]

MS84

Homogenization Theory for Neural Field Models

This talk is divided into two parts. In the first part wereview the derivation of the homogenized one - populationAmari equation by means of two - scale convergence tech-nique in the case of periodic microvariation in the connec-tivity function. In the second part we discuss the existenceand stability of single and multibump solutions of the ho-mogenized model.

John WyllerDepartment of Mathematical Sciences and TechnologyNorwegian University of Life [email protected]

MS84

Asymmetric Stationary Bumps in Neural FieldModels

For 1D neural field models, we show that the symmetry ofthe connectivity function causes a degeneracy, permittingthe existence of asymmetric bump solutions. When thegoverning nonlinear integral equation is transformed intoa higher-order ODE, the degeneracy leads to a conservedquantity. With this, we construct a horseshoe map andobtain infinitely many asymmetric/symmetric bump solu-tions. We then discuss the persistence of these solutionsunder perturbations of the connectivity function and thenonlinear gain.

Dennis YangDepartment of MathematicsDrexel [email protected]

MS85

Contact Network Models for Immunizing Infec-tions

Many infectious agents spread via close contact betweeninfected and susceptible individuals. The nature and struc-ture of interactions among individuals is thus of fundamen-tal importance to the spread of infectious disease. Het-erogeneities among host interactions can be modeled withcontact networks, and analyzed using tools of percolationtheory. Thus far, the field of contact network epidemiologyhas largely been focused on the impact of network struc-ture on the progression of disease epidemics. In this talk,we introduce network models which incorporate feedback

178 DS15 Abstracts

of the disease spread on network structure, and explore howthis feedback limits the potential for future outbreaks. Thishas implications for seasonal diseases such as influenza, andsupports the need for more adaptive public health policiesin response to disease dynamics.

Shweta BansalPenn State [email protected]

MS85

Mathematical Models of the Spatial and Evolution-ary Dynamics of Influenza A

The research areas of population biology and dynamicalsystems already have a fruitful shared history. Within this,disease modelling has been particularly lively for both itsrich dynamics and its practical importance. In this talk,we will have a brief tour of some of the types of models thatare in use for both the spatial and evolutionary aspects ofthe spread of influenza at the population level, and someof the future mathematical challenges.

Julia R. GogDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of [email protected]

MS85

A Multi-Scale Model of Multiple Exposures to aPathogen

Dose size and incubation period length are related for manyinfectious diseases. We explore a dose-dependent latentperiod of infection (a component of incubation period) fol-lowing multiple exposures to a pathogen, and study its ef-fect on disease transmission in a population. The immuno-epidemiological model is developed using a threshold-typedelay, which is transformed in a biologically natural way, toa system of differential equations with state-dependent de-lay. Bistability results, which has implications in infectioncontrol.

Jane HeffernanCentre for Disease Modelling, Mathematics & StatisticsYork [email protected]

Redouane QesmiYork [email protected]

Jianhong WuDepartment of Mathematics and StatisticsYork [email protected]

MS85

Evaluation of Combined Strategies for ControllingDengue Fever

Dengue is the most significant mosquito-borne viral infec-tion of humans, causing 50-100 million infections annually.The main line of attack against dengue has been traditionalmosquito control measures, such as insecticides. The com-ing years will see the broadening of our anti-dengue arse-nal to include genetically-modified mosquitoes, biocontrol

methods—such as Wolbachia—and vaccines. In this talk,I will discuss mathematical modeling that is being used tohelp design dengue control efforts using one, or a combina-tion, of these methods.

Alun LloydNorth Carolina State Universityalun [email protected]

MS86

Experimental Studies of Burning Invariant Mani-folds as Barriers to Reaction Fronts

We study Belousov-Zhabotinsky reaction fronts in the fol-lowing flows: (a) a single vortex flow; (b) a chain of oscil-lating vortices; and (c) extended vortex array or spatiallydisordered flows. In these flows, front propagation is im-peded and sometimes pinned by burning invariant mani-folds (BIMs) which act as one-way barriers. Experimentalmeasurements of barriers are compared with BIMs that arepredicted numerically. We consider the limits of validity ofthe BIM approach to more complicated flows.

Savannah GowenMount Holyoke College50 College Street, South Hadley, MA [email protected]

Tom SolomonBucknell [email protected]

MS86

Front Pinning in Single Vortex Flows

We study fronts propagating in 2D fluid flows and showthat there exist stable invariant front configurations forfairly generic flows. Here we examine the simple flow whichcombines a single vortex with an overall wind. Existenceof the stable front is related to the underlying fluid bifurca-tion. This elementary structure has application in chemicalreactor beds and laminar combustion in well-mixed fluids.

John R. MahoneyUniversity of California, [email protected]

Kevin A. MitchellUniversity of California, [email protected]

MS86

Propagation of An Autocatalytic Reaction Front inHeterogeneous Porous Media

We investigate experimentally and numerically the cou-pling of the propagation of an auto-catalytic reaction andthe flow in porous media. We will investigate the differentpropagation modes depending on the flow direction, its am-plitude and the disorder of the medium. More particularly,we will demonstrate that heterogeneity of the medium in-duces a rich variety of front dynamic and morphology.

Laurent TalonUniv. Paris-SudOrsay, F-91405, France

DS15 Abstracts 179

[email protected]

Dominique Salinlab. FAST, [email protected]

MS86

Front Propagation in Cellular Flows for Fast Reac-tion and Small Diffusivity

We investigate the influence of cellular flows on the propa-gation of Fisher-Kolmogorov-Petrovsky-Piskunov chemicalfronts in the limit of small molecular diffusivity and fastreaction i.e., large Peclet (Pe) and Damkohler (Da) num-bers. We develop an asymptotic theory that describes thefront speed in terms of a periodic path – an instanton –that minimizes a certain functional and yields closed-formresults for (log Pe)−1 Da Pe and Da Pe. Ourtheoretical predictions are compared with (i) numerical so-lutions of an eigenvalue problem and (ii) simulations of theadvection–diffusion–reaction equation.

Alexandra Tzella, Jacques VannesteSchool of MathematicsUniversity of [email protected], [email protected]

MS87

Geometric Optics and Piecewise Linear Systems

Light through a chessboard material with two different re-fractive indices (for black and white squares) is refractedand reflected in complicated ways. I will describe thederivation of a return map for a geometric ray obeyingSnell’s Law and use this to derive properties of the rays.

Paul GlendinningUniversity of [email protected]

MS87

Analysis of Traveling Pulses and Fronts in a Nons-mooth Neural Mass Model

We study the activity of coupled populations of excitatoryand inhibitory neurons in a neural firing rate model that in-cludes 1D nonlocal, spatial coupling. To facilitate analysisof spatio-temporal patterns, we approximate the (typicallysmooth) nonlinear firing rate function with the Heavisidestep function. We study the corresponding nonsmooth dif-ferential system in traveling wave coordinates, with a par-ticular interest in how the system transitions from travelingfront to pulse as the time-constant of inhibition increases.

Jeremy D. HarrisDepartment of MathematicsUniversity of [email protected]

MS87

Are Plankton Discontinuous, Smooth Or Slow-Fast(and Furious)?

In this talk, we first discuss a piecewise-smooth dynamicalsystem constructed for one predator feeding on two differ-ent types of prey and inspired by plankton observations.The piecewise-smooth model has a discontinuity between

the two vector fields. Thus, we then construct and discussdifferent smooth reformulations of the model and comparemodel predictions with data on freshwater plankton.

Sofia PiltzUniversity of [email protected]

MS87

Infinitely Many Coexisting Attractors in theBorder-Collision Normal Form

The nature of piecewise-linear maps (such as the tent map)facilitates exact calculations, yet such maps can displayextremely complicated dynamics (including chaos). Thistalk looks at two mechanisms by which two-dimensionalpiecewise-linear continuous maps can exhibit infinitelymany stable, or asymptotically stable, periodic solutionsat special points of parameter space. Scaling laws indi-cate the rate at which the number of coexisting attractorsdecreases with the distance from these points.

David J. SimpsonInstitute of Fundamental SciencesMassey [email protected]

MS88

Swarming of Self-propelled Particles in Fluids

Self propulsion, a distinction between active swarmers andpassive interacting particles, often invokes speed regula-tion strategies that can be essential for a swarm to developand maintain a certain flocking formation. However, speedregulation depends on the ability of a swarmer to sense itsown speed relative to its perceived surroundings. Here westudy a swarming system in low-Reynolds number flows,examining the effects of hampered speed regulation by thedisturbance flow on flock formations.

Yaoli ChuangCalifornia State University, [email protected]

Maria D’[email protected]

MS88

Origin and Structure of Dynamic Social NetworksBased on Cooperative Actions

Societies are built on social interactions. A novel theoret-ical framework to model dynamic social networks focusseson individual actions instead of interactions between indi-viduals and thereby eliminates the traditional dichotomybetween the strategy of individuals and the structure ofthe population. As a consequence, altruists, egoists andfair types are naturally determined by the local socialstructures, while globally egalitarian networks or stratifiedstructures arise. Cooperative actions drive the emergenceand shape the structure of social networks.

Christoph Hauert, Lucas WardilThe University of British Columbia

180 DS15 Abstracts


MS88

Hotspots in a Non-Local Crime Model

We extend the Short et al. burglary hotspot model to allowfor a larger class of criminal movement. Specifically, weallow criminals to travel according to a Levy flight ratherthan Brownian motion. This leads to a non-local systemof differential equations. The stability of the homogeneousstate is studied both numerically and through a Turing-type analysis. The hotspot profiles are then constructed toleading order in a singular regime.

Scott MccallaMontana State [email protected]

Jonah BreslauPomona [email protected]

Sorathan ChaturapruekHarvey Mudd Collegetum [email protected]


Daniel YazdiUniversity of California, Los [email protected]

MS88

Co-Dimension One Self Assembly

Self assembly refers to emergent behavior that oc-curs in systems with a large number of interactingmolecules or nanoparticles. These systems produce or-dered, supramolecular structures solely due to the interac-tions between their constituent molecules or particles. Mytalk will focus on mathematical models for physical pro-cesses, such as the assembly of inorganic polyoxometalate(POM) macroions into hollow spherical structures or theassembly of surfactant molecules into micelles and vesicles,where the supramolecular structure has co-dimension onecharacteristics. I will discuss both the mathematical the-ory that characterizes when such structures can arise, aswell as applications of these insights to physical models ofthese assemblies.

James von BrechtCalifornia State University, Long [email protected]

Scott MccallaMontana State [email protected]

David T. UminskyUniversity of San FranciscoDepartment of [email protected]

MS89

Network Reliability As a Tool for Using Dynamics

to Probe Network Structure

We apply the Moore-Shannon network reliability polyno-mial to infectious disease epidemiology on large social net-works. Special cases of the polynomial represent the prob-ability of cascading failures or epidemic outbreaks in com-plex networks. Although its exact evaluation is NP-hard,efficient, scalable Monte-Carlo estimation is practical. Aphysical interpretation supports analytical understandingof how local structures interact with dynamics to produceglobal function.

Stephen EubankVirigina Bioinformatics Institute, VA [email protected]

Yasamin KhorramzadehPhysics Dept.Virginia [email protected]

Mina YoussefVirginia Bioinformatics InstituteVirginia [email protected]

Shahir Mowlaei, Madhurima NathPhysics Dept.Virginia [email protected], [email protected]

MS89

Dynamical Macro-Prudential Stress Testing UsingNetwork Theory

We present a dynamic model to reveal the systemic struc-ture of a banking system, to analyze its sensitivity to ex-ternal shocks and to evaluate the presence of contagiousunderlying features of the system. As a case study, wemake use of the Venezuelan banking system in the periodof 1998–2013. The introduced model was able to capture,in a dynamic way, changes in the structure of the systemand the sensitivity of banks portfolio to external shocks.Results suggest the fruitfulness of this kind of approach topolicy makers and supervision agencies to address macro-prudential dynamical stress testing and regulation.

Dror Y. KenettBoston University, Physics [email protected]

MS89

Role of Netwok Topology in Collective OpinionFormation

To investigate the role of network structures on the phe-nomena of collective opinion formation, we investigate sev-eral modifications to the voter model on co-evolving net-works. For example we modify the rewiring step by a path-length-based preference for rewiring that reinforces localclustering and show that reinforcement of clustering in avoter model can have significant ramifications. Further-more, we will be employing this voter model dynamics toanalyze the structures of various empirical social networkdata sets.

Nishant MalikDepartment of MathematicsUniversity of North Carolina at Chapel Hill, NC, USA

DS15 Abstracts 181

[email protected]

MS89

Linear Dynamics on Brain Networks: A Tool forUnderstanding Cognition

Human cognitive function is a complex phenomenon thatoccurs via intricate neuronal dynamics evolving over asculpted anatomical network architecture housed withinthe skull. Yet, fundamental structural drivers of thesefunctions remain poorly understood. Drawing inspirationfrom network control theory, here we utilize a simple lin-ear model of brain dynamics on experimentally measuredanatomical networks to predict the role of brain areas (net-work nodes) in moving the brain into (i) easily reachablestates, (ii) difficult-to-reach states, and (iii) states thatrequire interactions between network communities, whichtraditionally map to cognitive systems including audition,vision, and motor systems. Our predictions map well toknown functions of brain areas, suggesting that structuralnetwork architecture forms a fundamental constraint onobserved cognitive processes underlying human thought.More broadly, our study illustrates the utility of dynamicmodels on networks to uncover critical drivers of systemfunction.

Danielle BassettSchool of Engineering and Applied ScienceUniversity of [email protected]

Fabio PasqualettiDepartment of Mechanical EngineeringUniversity of California, Riverside, [email protected]

MS90

The Dynamics of Alopecia Areata

Alopecia areata is an autoimmune disease causing distinctpatterns of hair loss. Little is known regarding the causesor treatment of the disease. We develop an ODE modelfor alopecia areata dynamics which incorporates one of thecurrent hypotheses that explains a range of experimentalobservations and suggests several avenues for treatment.Sensitivity analysis is used to determine which inputs havethe greatest influence helping focus the study on avenueswith the highest potential impact.

Atanaska DobrevaFlorida State [email protected]

Ralf PausUniversity of ManchesterUniversity of [email protected]

Nicholas CoganFlorida State [email protected]

MS90

Epistemic Uncertainty Quantification Using FuzzySet Theory

Epistemic uncertainty due to lack of knowledge is in-evitable in modeling and simulation. The existing stochas-

tic tools do not readily apply to epistemic uncertaintyquantification since probability distributions may not beavailable. In this paper, we propose a general three-stepprocedure based on fuzzy set theory to deal with epistemicuncertainty and extend it for mixed epistemic and aleatoryuncertainty quantification. The convergence rate of ob-tained numerical solutions is analyzed and demonstratedwith examples.

YanYan HeScientific Computing and Imaging CenterUniversity of [email protected]

Dongbin XiuUniversity of [email protected]

MS90

Using Sensitivity Analysis to Understand S. aureusInfections

The immune system is a complex network of interactionsthat challenges the technology and skills of biologists andmathematicians who study it. We present results fromglobal sensitivity analysis techniques (PRCC and Sobol’)for two different models, one ODE and one PDE, and dis-cuss the usefulness of these results for: model reduction,understanding immune system interactions, focusing dataassimilation techniques on parameters of interest, and mo-tivating biological experiments in the context of S. aureusinfections.

Angela M. JarrettFlorida State UniversityDepartment of [email protected]

Nick Cogan, M Yousuff HussainiFlorida State [email protected], [email protected]

MS90

Computational Aspects of Stochastic Collocationwith Multi-Fidelity Models

We shall discuss a numerical approach for the stochas-tic collocation method with multifidelity simulation mod-els. The method combines the computational efficiencyof low-fidelity models with the high accuracy of high-fidelity models. We shall illustrate the advantages of themethod via a set of more comprehensive benchmark ex-amples including several two-dimensional stochastic PDEswith high-dimensional random parameters. Finally, Wesuggest that tri-fidelity simulations with a low-fidelity, amedium-fidelity, and a high-fidelity model would be suffi-cient for most practical problems.

Xueyu ZhuScientific Computing and Imaging CenterUniversity of [email protected]

Dongbin XiuUniversity of Utah

182 DS15 Abstracts

[email protected]

MS91

Moreau Sweeping Processes on Banach Spaces

The sweeping process or Moreau’s process in a Hilbertspace H (introduced and studied by J.J. Moreau in J.D.E.in 1977) is an interesting problem in both Analysis andMechanics

−y(t) ∈ N(C(t); y(t)) a.e. in [0, T ], y(0) = y0 ∈ C(0)

where C(t) is a closed convex moving set depending on thetime t ∈ [0, T ] and y : [0, T ] → H is a BV mapping. Thereare a plethora of variants in this problem in Hilbert spaces.

In this talk I will present my last recent results on the ex-istence of solutions for several extensions to Banach spacesof Moreau sweeping processes and its variants. The mainproblems that will be presented are: For a given reflexivesmooth Banach space X,

(P1) Find y : [0, T ] → X∗ such that

⎧⎨⎩

− ddt(y(t)) ∈ N(C(t); J∗(y(t))) + F (t; J∗(y(t))) a.e. in [0, T ] and

J∗(y(t)) ∈ C(t),∀t ∈ [0, T ], and J∗(y(0)) ∈ C(0).


⎧⎨⎩

−y(t) ∈ N(C(t); J∗( ddt(y(t)))) + F (t; J∗(y(t))) a.e. in [0, T ] and

J∗( ddt(y(t))) ∈ C(t), a.e. on [0, T ], and J∗(y(0)) ∈ C(0), J∗( d

dty(0)) ∈ C(0).


⎧⎨⎩

− ddt(y(t)) ∈ N(C(t, J∗(y(t)));J∗(y(t))) a.e. in [0, T ] and

J∗(y(t)) ∈ C(t, J∗(y(t))),∀t ∈ [0, T ], and J∗(y(0)) ∈ C(0, J∗(y(0))).

Here J∗ is the normalized duality mapping in X∗ definedfrom X∗ to X by

J∗(x∗) = {j∗(x∗) ∈ X : 〈x∗, j∗(x∗)〉 = ‖j∗(x∗)‖‖x∗‖ = ‖x∗‖2 = ‖j∗(x∗)‖2}.

Messaoud BounkhelDepartment of MathematicsKing Saud University, Saudi [email protected]

MS91

Periodic Solutions of Moreau Sweeping Processesand Applications

The concept of equilibrium has been introduced by O.Makarenkov in recent studies of the following autonomusMoreau sweeping process:

−u′(t) ∈ NB(u(t)) + f(u(t)).

In the case of periodically perturbed f there exists a so-lution in the neighbourhood of the equilibrium. By usingcontraction mapping theory it is possible to prove stabil-ity of closed orbit for a prototypic sweeping process in aHilbert space.

Ivan GudoshnikovDepartment of Mathematical SciencesUniversity of Texas at Dallas

[email protected]

MS91

Evolution Equations Governed by Sweeping Pro-cesses and Applications in Heat Equations withControlled Obstacles

In this talk, we provide results on existence, stability andoptimality conditions for the following class of evolutionequations

−x(t) ∈ ∂Φ(x(t))+N(x(t);C(t, u(t))) a.e. t ∈ [0, T ]; x(0) = x0.

We then apply these results for heat equations with con-trolled obstacles. This talk bases on joint work with JuanPeypouquet and Luis M. Briceno-Arias.

Hoang NguyenDepartment of MathematicsUniversity of Technical Federical Santa Maria, [email protected]

MS91

Sweeping Process and Congestion Models forCrowd Motion

We propose a mathematical model of crowd motion inemergency evacuation. This microscopic model takes intoaccount the local interactions between pedestrians. Theunderlying evolution problem takes the form of a first orderdifferential inclusion.and its well-posedness can be provedwith the help of recent results concerning sweeping processby uniformly prox-regular sets. Furthermore, we proposea numerical scheme (adapted from Moreau’s catching-upalgorithm) and prove its convergence.

Juliette VenelLab de Mathematiques et leurs Applications deValenciennesUniversite Lille-Nord de [email protected]

MS92

Braid Dynamics, Self-organized Criticality, and So-lar Coronal Heating

Magnetic field lines in the atmosphere of the sun are an-chored at the surface, and exist in a highly conductingenvironment. Hence their topological structure can onlychange gradually via surface motions, or violently via flar-ing events. We present models for the evolution of the braidstructure to a self-organized state. The discrete nature ofthe flux distribution at the surface enhances the resultingenergy dissipation.

Mitchell BergerDepartment of MathematicsUniversity of [email protected]

MS92

Characterizing Complexity of Aperiodic Braids ofTrajectories

A braid of trajectories is an algebraic model of the se-quence of interchanges of particles advected by a flow. In-sights based on braid-theoretic arguments typically requireperiodicity of analyzed trajectories. This talk explores

DS15 Abstracts 183

what can be deduced from generic, non-periodic trajecto-ries sampled from a flow. We define an aperiodic quantifierof braid complexity and present its dependence on flow pa-rameters, on number of trajectories analyzed, and discussconnections to topological entropy.

Marko BudisicUniversity of Wisconsin-MadisonDepartment of [email protected]

Jean-Luc ThiffeaultDept. of MathematicsUniversity of Wisconsin - [email protected]

MS92

Topological Shocks in Burgers Turbulence

We shall discuss statistical properties of global solutionsto the random forced Burgers equation. The problem isclosely related to analysis of minimizers for random time-dependent Lagrangian systems. We show that for suchsystems on compact manifolds there exists a unique globalminimizer. We also discuss dynamical properties of shocksand show that their global structure is quite rigid and re-flects the topology of the configuration manifold

Kostantin KhaninDepartment of MathematicsUniversity of [email protected]

MS92

Topology of Vortex Trajectories in Wake-LikeFlows

Complex vortex patterns can emerge downstream of bluffbodies as the result of fluid-structure interaction. As inmany fluid systems, the vortex cores define regions thatremain coherent for relatively long times. Using a reduced-order model of the dynamics, the topological complexity ofthe flow is examined through braiding of the vortex trajec-tories. This wake-like model provides an example of howtopological chaos may occur naturally through the dynam-ics of coherent structures.

Mark A. StremlerBiomedical Engineering and MechanicsVirginia [email protected]

MS93

On the Generation of Spiral and Scroll Waves byPeriodic Stimulation of Excitable Media in thePresence of Obstacles of Minimum Size

In this work we consider the periodic stimulation of twoand three dimensional excitable media in the presence ofobstacles. We focus our attention in the understanding ofthe minimum size obstacles that allow generation of spiraland scroll waves, and describe different mechanisms thatlead to the formation of such waves. The present stud-ies might be helpful in understanding and controlling theappearance of spiral and scroll waves in the medium.

Daniel OlmosDepartment of MathematicsUniversidad de Sonora

[email protected]

Humberto OcejoUniversidad de [email protected]

MS93

Interaction of Electric Field Stimuli with ScrollWaves in Three Dimensions

An applied electric field interacts differently with an actionpotential scroll wave depending on its orientation with thescroll wave’s filament. In particular, defibrillation charac-teristics of the electric field are often more favorable whenoriented parallel to the filament, particularly in the caseof a thin medium. Theory and computer simulations willbe presented illustrating the dynamics of the scroll-wave-electric-field interaction and its dependence on wall thick-ness and field orientation.

Niels OtaniRochester Institute of [email protected]

Valentin KrinskiINLN,CNRS, [email protected]

MS93

Describing Scroll Wave Ring Interactions Via In-teracting Potentials

We study the dynamics of scroll rings using a simplifiedmodel of cardiac action potential (the Karma model) thatproduces scroll waves with circular core at high excitability(positive tension regime). We calculate the trajectories ofsymmetric scroll rings as a function of core radius and dis-tance to a bottom boundary and derive a potential functionthat can then be used to characterize and predict the dy-namics without the need for integrating the whole system.

Flavio M. FentonGeorgia Institute of [email protected]

Jairo RodriguezUniversidad de [email protected]

Daniel OlmosDepartment of MathematicsUniversidad de [email protected]

MS93

Unusually Simple Way to Create Spiral Wave inAn Excitable Medium

Our analytical and numerical results indicate that a suffi-ciently strong jump in the diffusion coefficient can resultin a unidirectional propagation block in a nonuniform ex-citable medium. This phenomenon can be used to createspiral wave in a two-dimensional medium with a specificsize and geometry of the inhomogeneity. Following thisway the spiral wave can be created simply after a singleexcitation stimulus while others known methods need at

184 DS15 Abstracts

least two stimuli.

Vladimir Zykov, Alexei KrekhovMax Planck Institute for Dynamics and [email protected], [email protected]

Eberhard BodenschatzMax Planck Institute for Dynamics & [email protected]

MS94

Narrow Escape to Traps with Absorbing and Re-flecting Portions

We study the Narrow Escape Problem to a small trap witha mixed configuration of absorbing and reflecting sections.In the limit of small trap radius, we derive a high order ex-pansion for the mean survival time which incorporates theasymmetry of the trap through an orientation term. Theorientation of the trap is found to significantly influencecapture time, particularly in the scenario where the trap isundergoing prescribed motion.

Alan E. LindsayApplied Computational Mathematics and StatisticsUniversity of Notre [email protected]

MS94

Sampling First-Passage Events When Drift Is In-cluded in the First-Passage Kinetic Monte CarloMethod

We have developed a method for simulating stochasticreaction-drift-diffusion systems, where the drift arises frompotential fields. The method combines elements of theFirst-Passage Kinetic Monte Carlo (FPKMC) method forreaction-diffusion systems and the Wang-Peskin-Elston lat-tice discretization of drift-diffusion. The original FP-KMC uses analytic solutions of the diffusion equation andtherefore cannot include nonlinear drift. In our method(Dynamic Lattice FPKMC), each molecule undergoes acontinuous-time random walk on its own adaptive lattice.

Ava MauroApplied and Computational Math and StatsUniversity of Notre [email protected]

Samuel A. IsaacsonBoston UniversityDepartment of Mathematics and [email protected]

MS94

Uniform Asymptotic Approximation of Diffusion toa Small Target

The problem of the time required for a diffusing moleculewithin a large bounded domain to first locate a small tar-get is prevalent in biological modeling. I consider thisproblem for a small spherical target. Uniform in timeasymptotic expansions in the target radius of the solu-tion to the corresponding diffusion equation is developed.The approach is based on combining short-time expansionsusing pseudo-potential approximations with long-time ex-pansions based on first eigenvalue and eigenfunction ap-proximations. These expansions allow the calculation of

corresponding expansions of the first passage time densityfor the diffusing molecule to find the target.

Jay NewbyMathematical Biosciences InstituteThe Ohio State [email protected]

MS94

Drunken Robber, Tipsy Cop: First Passage Times,Mobile Traps, and Hopf Bifurcations

For a random walk on a confined one-dimensional domain,we consider mean first passage times in the following twoscenarios: a randomly moving trap and an oscillating trap.In both cases, we find that a stationary trap actually per-forms better than a very slowly moving trap; however, atrap moving sufficiently fast performs better than a sta-tionary trap. Also, we will show the connection betweenMFPT and Hopf-bifurcation in Gray-Scott model.

Justin C. TzouDalhousie [email protected]

Shuangquan XieMathematics and StatisticsDalhousie [email protected]


MS95

A Dynamical Switching of Reactive and Nonreac-tive Modes at High Energies

In Hamiltonian systems, the reaction coordinate, the de-gree of freedom along which reaction proceeds, has beenconsidered to be unchanged independent of the total en-ergy of the system. I will present our recent finding that,for more than two degrees of freedom Hamiltonian systems,the identity of reaction coordinate can change, in general,as a function of the total energy of the system throughthe breakdown of normally hyperbolic invariant manifoldlocated around the saddle.

Tamiki KomatsuzakiHokkaido [email protected]

Mikito TodaNara Women’s [email protected]

Hiroshi TeramotoHokkaido [email protected]

MS95

Control of a Model of DNA Opening Dynamics viaResonance with a Terahertz Field

We study the internal resonance, energy transfer, and con-trol of DNA opening dynamics via parametric resonance.The model is a chain of pendula in Morse potential thattakes into account helicity, inhomogeneity, and environ-

DS15 Abstracts 185

mental effects. While the model is robust to noise, wedemonstrate the possibility of triggering its opening dy-namics by targeting certain internal modes with specificterahertz fields. This may suggests that DNA natural dy-namics can be significantly affected by terahertz radiationexposures.

Wang-Sang KoonCalifornia Institute of [email protected]

MS95

Obtaining Coarse-Grained Models from MultiscaleData

In many applications it is desirable to infer stochasticcoarse-grained models from observational data of a multi-scale process. Estimators such as the maximum likelihoodestimator can, however, be strongly biased in this setting.In this talk we discuss a novel inference methodology thatdoes not suffer from this drawback. Moreover, we exem-plify through a real-world data set how these data-drivencoarse-graining techniques can be used to study the statis-tical properties of a given temporal process.

Sebastian Krumscheid

Ecole Polytechnique Federale de Lausanne (EPFL)[email protected]

Greg PavliotisImperial College [email protected]

Serafim KalliadasisDepartment of Chemical EngineeringImperial College [email protected]

MS95

Mode-Specific Effects in Structural Transitions ofAtomic Clusters with Multiple Channels

We present the dynamical origin of mode-specific effectsin structural transitions of atomic clusters with multiplechannels. We employ the hyperspherical coordinates toidentify reactive modes and driving modes for the respec-tive channels of structural transitions. It is shown thatthe branching ratios among different channels depend sig-nificantly on the modes that are initially activated. Suchmode-specific branching ratios are explained in terms of thedynamical coupling and energy transfer between reactivemodes and driving modes.

Tomohiro YanaoWaseda [email protected]

MS96

Discrete Breathers in Vibro-Impact Lattice Models

Vibro-impact models offer a unique opportunity for ob-taining exact analytic solutions for discrete breathers inone-dimensional and two-dimensional systems (with triv-ial possibility of generalization for 3D case). The solutionsare obtained both for Hamiltonian models and for theirforced/damped counterparts. Moreover, a formalism basedon saltation matrices allows efficient analysis of global sta-

bility patterns for such breather solutions.

Itay GrinbergFaculty of Mechanical EngineeringTechnion - Israel Institute of [email protected]

Oleg GendelmanTechnion Israel Institute of [email protected]

MS96

Stable Two-Dimensional Solitons in Free Space:Gross-Pitaevskii Equations with the Spin-OrbitCoupling


Boris MalomedDepartment of Physical Electronics, Faculty of Engr.Tel Aviv University, 69978 [email protected]

MS96

Nonlinear Dynamics of Non-Stretched Membrane

We present the analytical study of resonance non-stationary dynamics in the discrete initially non-stretchedmembrane. The model consists of the weightless stringwith n attached masses which are supported in turn by northogonal weightless strings. It is shown that the intenseenergy exchange(nonlinear beats) in such discrete mem-brane can be realized between different parts of the sys-tem (effective particles). Its analytical description is ob-tained in terms of limiting phase trajectories (LPT) withusing the non-smooth transformations. The LPT boundsthe domain of ordered motion in the phase space of thesystem. Increase of the excitation energy leads to two dy-namical transitions caused by instability of one of nonlin-ear normal modes and LPT, respectively. As a result ofthe second transition the non-stationary energy localiza-tion arises. The obtained analytical solutions are confirmedby numerical simulations.

Leonid ManevichSemenov Institute of Chemical PhysicsRussian Academy of [email protected]

MS96

Mixed Solitary Shear Waves in a Granular Net-work

We study primary pulse transmission in two-dimensionalgranular networks and predict a new type of mixed nonlin-ear solitary pulses shear waves, and pulse equi-partitionbetween the chains of the network. An analytical model isasymptotically studied, based on the one-dimensional non-linear mapping technique of Starosvetsky. To confirm thetheoretical predictions we experimentally tested a series oftwo-dimensional granular networks, and validated the oc-currence of strong energy exchanges and equi-partition forsufficiently large number of beads.

Yijing ZhangUniversity of Illinois at [email protected]

186 DS15 Abstracts

Md. Arif HasanMechanical Science and EngineeringUniversity of [email protected]

Yuli StarosvetskyTechnion, Israel Institute of [email protected]

D. Michael McFarland, Alexander VakakisUniversity of [email protected], [email protected]

MS97

Cyclic Drug Delivery Devices and Monotone Dy-namical Systems

In the case of a gel membrane geometry, we show existenceof oscillatory solutions corresponding to the system oscil-lating between the collapsed and the swollen phases, as theionic concentration reaches a critical threshold. We applythe theory to the design of a cyclic drug delivery device ac-tivated by a chemical reaction that releases the positivelycharged ions that trigger the volume transition.

Maria-Carme CaldererDeparment of MathematicsUniversity of Minnesota, [email protected]

MS97

Evaluation of the Diffusion Coefficient of Nanopar-ticles Using Mathematical Simulation

We developed a novel, non-expensive nanoparticle (NP)drug-carrying system produced by self-assembly. A majorobjective was to evaluate the NP diffusion properties. Tocharacterize their drug-release properties drug-loaded par-ticles were placed in the donor of a double-compartmentdiffusion cell and the drug concentration in the receiverwas sampled periodically. In this study we show a mech-anistic model and mathematical simulation that, coupledwith the experimental results, was used to evaluate thenanoparticle diffusion coefficient.

Giora EndenDepartment of Biomedical Engineering, [email protected]

Amnon SintovDepartment of Biomedical Engineering, [email protected]

MS97

Viscoelastic Effects in Drug Delivery

Classical models of Hookean solid and Newtonian liquidmay be insufficient for description of biological fluids andmaterials used in controlled drug delivery. Instead, differ-ent viscoelastic models may be appropriate. We present anumber of examples where viscoelasticity effects are signifi-cant. Among them are: (i) non-Fickian drug release from aswelling polymer particle; (ii) dynamics of a pore in a lipidmembrane; (iii) drug delivery through a mucus layer in pul-monary airways. The support of the US-Israel Binational

Science Foundation (grant No. 2008122) is acknowledged.

Alexander NepomnyashchyDepartment of [email protected]

Vladimir A. VolpertNorthwestern [email protected]

Yulia KanevskyTechnion - Israel Institute of [email protected]

MS97

Fluid Flow and Drug Delivery in a Brain Tumor

We consider the problem of steady/unsteady fluid flow anddrug delivery in a growing brain tumor. Objective is tounderstand the physiology of fluid flow and examine theeffect of concurrent application of two anti-cancer drugsin a brain tumor. Therapeutic Index, which is a measureof efficiency of drug delivery in the tumor, is determinedfor different values of the parameters and discussed in theabsence or presence of drugs’ interactions.

Ranadhir RoyUniversity of Texas-Pan [email protected]

Daniel RiahiUniversity of Texas - Pan [email protected]

MS98

HIV Viral Rebound Times Following Suspension ofArt: Stochastic Model Predictions

Suspension of antiretroviral treatment (ART) for HIV typ-ically leads to rapid viral load rebound to pre-treatmentlevels. However, reports suggest that early ART initiationmay delay viral rebound, for months, years, or permanently(post-treatment control, PTC), after ART suspension. Wepresent a model of post-treatment HIV dynamics. Froma branching process formulation we derive viral reboundtime probability densities and the probability of PTC. Us-ing these, we discuss viral rebound times and conditionsfor PTC.

Jessica M. ConwayPennsylvania State [email protected]

MS98

Modeling HCV Infection: Viral Dynamics andGenotypic Diversity

Hepatitis C virus (HCV) is present in the host with multi-ple variants generated by its error prone RNA-dependentRNA polymerase. We developed a series of models of viraldynamics for non-overlapping generations, based on differ-ence equations, that allows us to follow the diversificationof HCV virus early on during infection. We compared theanalytical solutions of these models with a more detailedagent-based model of the HCV lifecycle. We found thatthe simplified model describes infection well, as long as

DS15 Abstracts 187

saturation effects are not present. We then compared thepredictions of these models with data from acute infectionin 9 plasma donors, with frequent sampling early in infec-tion.

Ruy M. RibeiroTheoretical Biology and BiophysicsLos Alamos National [email protected]

MS98

Modeling Equine Infectious Anemia Virus Infec-tion: Virus Dynamics, Immune Control, and Es-cape

Equine Infectious Anemia Virus is a retrovirus that estab-lishes persistent infection in horses. Mathematical mod-els of within-host infection dynamics including immune re-sponses will be presented. Analysis of the models yieldsthresholds that would be necessary for immune responsesto successfully control infection. Furthermore, model re-sults predict the conditions under which multiple compet-ing strains coexist or a subdominant viral strain escapesantibody neutralization and dominates the infection. Nu-merical simulations are presented to illustrate the results.

Elissa SchwartzWashington State [email protected]

MS98

Modeling HIV Infection Dynamics under Condi-tions of Drugs of Abuse

Drugs of abuse are associated with higher viral loads andlower host-immune responses in HIV-infected drug abusers.To explore effects of drugs of abuse on HIV infection, I willpresent dynamical system models that agree well with ex-perimental data from simian immunodeficiency virus infec-tions of morphine-addicted macaques. Using our models,we evaluate morphine-induced alterations in target cell sus-ceptibility and HIV-specific immune response that result inhigher viral replications and accelerated disease progres-sions.


MS99

The Domain Dependence of Chemotaxis in a Two-Dimensional Turbulent Flow

Coherent structures are ubiquitous in environmental andgeophysical flows. Recent advances in the identification offinite-time transport barriers have enabled the extractionof organizing templates for passive scalars in the limit ofinfinitesimal diffusion. In this presentation, we try to re-late Lagrangian mixing and its corresponding measures toreaction processes in turbulent flows. Using a specific ex-ample of chemotaxis process in turbulence, we demonstratethat elliptic regions of the flow trigger higher uptake ad-vantage for motile species of microorganisms. We analyzehow the flow field and the relevant flow topology lead to

such a relation.

Kimberley JonesSchool of Mathematical & Statistical SciencesArizona State University, Tempe, AZ, [email protected]

Wenbo TangArizona State [email protected]

MS99

Flow and Grow: Experimental Studies of Time-Dependent Reaction-Diffusion-Advection Systems

When a reaction-diffusion-advection system becomes non-autonomous, a new dimensionless parameter emerges: γ,the ratio of growth to flow timescales. For γ ∼ 1, the in-teraction between growth and flow can produce complexresonance phenomena. My team and I have developed anexperimental apparatus capable of simultaneous measure-ments of velocity fields and front locations in RDA. I willpresent studies varying γ = 1 and discuss implications forphytoplankton growth in Earth’s oceans, where γ = 0.8.

Douglas H. KelleyUniversity of Rochester218 Hopeman Engineering Building Rochester, [email protected]

MS99

Lagrangian Coherent Structures for ReactionFronts in Unsteady Flows

Recent theoretical and experimental investigations havehighlighted the role of invariant manifolds, termed burn-ing invariant manifolds (BIMs), as one-way barriers toreaction fronts propagating through time-independent ortime-periodic flows. This talk extends the concept of BIMsto unsteady flows, thereby constructing coherent struc-tures that organize and constrain the propagation of re-action fronts through general flows. Following Farazmand,Blazevski, and Haller [Physica D 278279, 44 (2014)], wecharacterize coherent structures as curves of minimal La-grangian shear.



MS99

Transport in Chaotic Fluid Convection

Many interesting problems can be formulated as a diffusingconcentration field that is also advected by a complex fluidflow in a large spatially-extended domain. We explore thecase where this field is also reacting, as in chemical andcombustion problems, or motile, as in bioconvection. Us-ing large-scale parallel numerical simulations we quantifythe dynamics of a propagating front in a chaotic flow fieldand the complex patterns of bioconvection for conditions

188 DS15 Abstracts

accessible to experiment.

Mark PaulDepartment of Mechanical EngineeringVirginia [email protected]

MS100

Some Nonsmooth Problems Inspired by Concep-tual Climate Models

In this talk, I’ll outline the development of a global en-ergy balance model that includes ice-albedo feedback andgreenhouse gas effects. I’ll explore how the choice oftemperature-dependent albedo affects transitions betweenstable steady states and periodic orbits of the system byapplying modern techniques from nonsmooth dynamicalsystems.

Anna M. BarryInstitute for Mathematics and its ApplicationsUniversity of [email protected]

MS100

Continuation of Chatter in a Mechanical Valve

This presentation considers the analysis of periodic chat-ter in a mechanical pressure-relief valve, with emphasison global interactions associated with a Shilnikov bifurca-tion. It reviews work in non-smooth systems by Piiroinenand Nordmark for the numerical parameter continuationof periodic orbits with infinitely many switches in finitetime, using forward integration and nonlinear root solvers,and describes an alternative formulation expressed in termsof coupled boundary-value problems, implemented in theCOCO framework.

Harry DankowiczUniversity of Illinois at Urbana-ChampaignDepartment of Mechanical Science and [email protected]

Erika FotschUniversity of Illinois at [email protected]


MS100

Lost in Transition: Nonlinearities in the Dynamicsof Switching

When a system transitions abruptly from one behaviourto another, empirical models often describe well what hap-pens just after and just before the transition, but not dur-ing. Worse, attempts to model the switch itself may in-volve complex higher dimensional and smaller scale pro-cesses. We can access the hidden dynamics of the transi-tion, though, using simple dynamical principles. To do sofully requires a nonlinear theory of transitions in piecewisesmooth dynamical systems.

Mike R. JeffreyUniversity of Bristol

[email protected]

MS100

Grazing Bifurcations in Engineering and MedicalSystems


Marian WiercigrochUniversity of AberdeenKing’s [email protected]

MS101

Nonlinear Dynamics of Variational Data Assimila-tion

Using the path integral formulation of statistical data as-similation, we show how to find the consistent global min-imum path, show its dependence on the number of mea-surements at each observation time, and demonstrate thatin certain parameter regimes, the corrections to the varia-tional approximation is small and computable.

Henry D. AbarbanelPhysics DepratmentUniv of California, San [email protected]

Kadakia [email protected]

Jingxin YeDepartment of PhysicsUniversity of California at San [email protected]

Uriel I. Morone, Daniel [email protected], [email protected]

MS101

Attractor Comparisons Based on Density

In this work a chaotic attractor is described as a densitydistribution in phase space. Describing the attractor asa density allows attractors to be compared using a smallnumber of coefficients. Fits of these comparison coefficientsas a function of some parameter change in the attractorcan be used to predict how the attractor will change as aparameter changes. These density comparisons are usedhere to detect nonlinearity in a simple electronic circuit orto track parameter changes in a circuit based on the Rosslersystem. Comparisons between attractors could be usefulfor tracking changes in an experiment when the underlyingequations are too complicated for vector field modeling.

Thomas L. CarrollNaval Reseach [email protected]

MS101

Manifold Learning Approach for Modelling Col-lective Chaos in High-Dimensional Dynamical Sys-

DS15 Abstracts 189

tems

It has been known that a certain dynamical system exhibitslower-dimensional motion at a macroscopic level whereasit also keeps high-dimensional chaos at a microscopic level,called collective chaos. In this study, we propose an ap-proach based on manifold learning in order to extract vari-ables constructing nonlinear coordinate to the attractor ofcollective chaos. We apply the proposed approach to mod-els including sparse networks of chaotic maps and leakyintegrate-and-fire neurons.

Hiromichi SuetaniDepartment of Physics and AstronomyKagoshima [email protected]

MS101

Precision Variational Approximations in StatisticalData Assimilation

Data assimilation (DA) comprises transferring informationfrom observations of a complex system to physically-basedsystem models with state variables x(t). Typically, the ob-servations are noisy, the model has errors, and the initialstate of the model is uncertain, so the DA is statistical.One can thus ask questions about expected values of func-tions 〈G(X)〉 on the model path X = {x(t0), . . . ,x(tm)} asit moves through an observation window {t0, . . . , tm}. Theprobability distribution on the path P (X) = exp[−A0(X)]determines these expected values. Variational methodsseeking extrema of the ‘action’ A0(X) are widespread forestimating 〈G(X)〉 in many fields of science. In a pathintegral formulation of statistical DA, we consider vari-ational approximations in a standard realization of theaction where measurement and model errors are Gaus-sian. We (i) discuss an annealing method for locating thepath X0 giving a consistent global minimum of the ac-tion A0(X

0), (ii) consider the explicit role of the numberof measurements at each measurement time in determin-ing A0(X

0), and (iii) identify a parameter regime for thescale of model errors which allows X0 to give a preciseestimate of 〈G(X0)〉 with computable, small higher ordercorrections.

Jingxin YeDepartment of PhysicsUniversity of California at San [email protected]

MS102

Shadow Networks: Discovering Hidden Nodes withModels of Information Flow

Complex, dynamic networks underlie many systems, andunderstanding these networks is the concern of a great spanof important scientific and engineering problems. Quanti-tative description is crucial for this understanding yet, dueto a range of measurement problems, many real networkdatasets are incomplete. Here we explore how accidentallymissing or deliberately hidden nodes may be detected innetworks by the effect of their absence on predictions of thespeed with which information flows through the network.We use Symbolic Regression (SR) to learn models relatinginformation flow to network topology. These models showlocalized, systematic, and non- random discrepancies whenapplied to test networks with intentionally masked nodes,demonstrating the ability to detect the presence of missingnodes and where in the network those nodes are likely to

reside.

James BagrowDepartment of Mathematics & StatisticsUniversity of [email protected]

MS102

A Network Measure for the Analysis and Visual-ization of Large-Scale Graphs

Given an undirected graph, we describe a two-dimensionalinteger-valued measure, the Q-matrix, based on the con-nected component size distribution of its degree-limitedsubgraphs. This generalization of the degree distributionyields a small sparse matrix representing the number ofweakly connected components of a particular size duringa prescribed percolation process. When viewed as a two-dimensional histogram, this landscape yields a canonic vi-sual representation, i.e. an identification portrait, revealingimportant network properties.

Roldan PozoNational Institute of Standards and Technology, [email protected]

MS102

Revealing Collectivity in Evolving Networks: ARandom Matrix Theory Approach

Networks are the result of the tangled interconnectionsamong their nodes. As the network evolves, group of nodesoften undergo similar evolution patterns, giving rise to col-lective behavior. Here, we aim to uncover and quantify thedegree of collectivity in the evolution of a complex network.In particular, we use Random Matrix Theory to identifysignificant correlations between the temporal topologicalproperties (e.g. degree, centrality) of nodes. We apply ourmethod to both functional networks, obtained from stocksand climate correlation data, and structural networks, ob-tained from Internet AS-level connectivity data.

Saray ShaiDepartment of MathematicsUniversity of North Carolina at Chapel [email protected]

MS103

On the Computation of Attractors for Delay Dif-ferential Equations

In this talk we will introduce a numerical method whichallows to approximate (low dimensional) invariant sets forinfinite dimensional dynamical systems. We will particu-larly focus on the computation of attractors for delay dif-ferential equations. The numerical approach is inherentlyset oriented - that is, the invariant sets are computed by asequence of nested, increasingly refined approximations -,and does not rely on long term simulations of the underly-ing system.

Michael DellnitzUniversity of Paderborn, Germany

190 DS15 Abstracts

[email protected]

MS103

Computing Coherent Sets in Turbulent Systems

In time dependent dynamics, it is often possible to dividephase space into sets which are seperated by transport bar-riers. Finding these sets helps to understand the globaldynamical behavior of systems arising in, e.g. atmosphericflows, plasma physics and biological models. In this talkwe present a new approach for the computation of coher-ent sets by incorporating time-continuous diffusion into themodel. This leads to an advection-diffusion equation (theFokker-Planck equation) whise solution we approximateusing spectral collocation. The approach does not needany particle trajectories and is therefore suited for systemswhere these are hard to obtain, e.g. turbulent systems.

Andreas DennerCenter for MathematicsTechnische Universitaet [email protected]

Oliver JungeCenter for MathematicsTechnische Universitaet Muenchen, [email protected]

MS103

The Geometry of Lagrangian Coherent Structures

We propose a novel, geometric method to identify subsetsof phase space that retain small boundary size relativeto volume as they are evolved by a nonlinear dynamicalsystem. We describe a computational method to identifycoherent sets based on eigenfunctions of a new dynamicLaplacian operator. Finally, we demonstrate that the dy-namic Laplacian operator can be realised as a zero-diffusionlimit of the classical probabilistic method for finding coher-ent sets, which is based on small diffusion.

Gary FroylandUNSW [email protected]

MS103

Coherent Families: Spectral Theory for TransferOperators in Continuous Time

The decomposition of the state space of a dynamical sys-tem into metastable or almost-invariant sets is importantfor understanding macroscopic behavior. This concept iswell understood for autonomous dynamical systems, andhas recently been generalized to non-autonomous systemsvia the notion of coherent sets. We elaborate here on thetheory of coherent sets in continuous time for periodically-driven flows and describe a numerical method to find pe-riodic families of coherent sets without trajectory integra-tion.

Peter KoltaiFree University [email protected]

Gary FroylandUNSW Australia

[email protected]

MS104

Finite-Time Lagrangian Transport Through Sur-faces in Volume-Preserving Flows

We present a Lagrangian approach to the quantification oftransport of conserved quantities through a given hyper-surface in general time-dependent, n-dimensional volume-preserving flows. This is of significant importance for (i)the calculation of coherent transport by Lagrangian mate-rial sets such as coherent vortices in geophysical fluid flows,and (ii) semi-Lagrangian approaches to numerically solvingscalar advection equations.

Daniel KarraschETH Zurich, [email protected]

MS104

A Direct Method for Computing Failure Bound-aries of Non-autonomous Systems

We present an efficient method, based on continuation of atwo-point boundary value problem, to investigate the pa-rameter dependence of system behaviour for models thatare subject to an external forcing. As an example we con-sider a model of a post-tensioned self-centring frame thatexperiences an earthquake. The failure boundary is theboundary of the region in the space of possible earthquakesfor which the frame displacement remains within a givenrange.

Hinke M. OsingaUniversity of AucklandDepartment of [email protected]

MS104

Interactions Between Noise and Rate-Induced Tip-ping

A non-autonomous system passes a tipping point whengradual changes in input levels cause the output to changesuddenly. I investigate a new way to help detect tippingbefore it occurs. For rate-induced tipping, analysing howmuch the system deviates from the quasi-steady state equi-librium gives an early-warning indicator. I show that early-warning indicators are present as soon as the most likelypath for escape deviates from the quasi-steady state.

Paul RitchieUniversity of ExeterMathematics research [email protected]

MS104

Rate-Induced Bifurcations in Slow-Fast Systems

Rate-induced bifurcations describe the failure to track amoving stable state in systems with drifting parameters.Unlike classical bifurcations, they occur only above somecritical drift rate. We investigate rate-induced bifurcationsin slow-fast systems, using the theory of folded singulari-ties and canards, to uncover thresholds with intricate bandstructures, separating initial states that track the mov-ing stable state from those that destabilise. These novel

DS15 Abstracts 191

thresholds explain non-obvious tipping point and excitabil-ity phenomena that often puzzle scientists.

Sebastian M. WieczorekUniversity of ExeterMathematics Research [email protected]

MS105

First Passage Time Problems for Stochastic HybridSystems

We review recent work on the analysis of first-passage timeproblems in stochastic hybrid systems. A stochastic hybridsystem involves the coupling between a piecewise determin-istic dynamical system and a time-homogeneous Markovchain on some discrete space. Examples include voltage-gated ion channels, intermittent transport by molecularmotors, and stochastic neural networks. We construct apath-integral representation of solutions to the underlyingmaster equation, and use this to derive a large deviationprinciple for escape problems. We show that the result-ing Hamiltonian is given by the principle eigenvalue of alinear operator that depends on the transition rates of theMarkov chain and the nonlinear functions of the piecewisedeterministic system.


MS105

Exploration and Trapping of Mortal RandomWalkers

The calculation of first passage times has a long history,more recently extended to ”anomalous” walks (subdiffu-sive or superdiffusive) in addition to those that lead to or-dinary diffusion. However, the possible death of a walkerbefore reaching its target has only recently been consid-ered. Evanescence obviously profoundly affects quantitiessuch as the survival probability of a target. I will talk aboutthe effects of evanescence on first passage properties.

Katja LindenbergDepartment of Chemistry and BiochemistryUniversity of California San Diego, [email protected]

Santos B. Yuste, Enrique AbadUniversidad de [email protected], eabad@unex es

MS105

Trajectory-to-Trajectory Fluctuations in the First-Passage Phenomena in Bounded Domains

We propose a novel method to quantify the trajectory-to-trajectory fluctuations of the first passage of a Brownianmotion (BM) to targets on the boundary of compact do-mains, based on the distribution of the uniformity index,measuring the similarity of the first passage times of twoindependent BMs starting at the same location. This anal-ysis permits us to draw several general conclusions aboutthe importance of the trajectory-to-trajectory fluctuationson the first-passage behavior.

Gleb Oshanin

Laboratoire de physique theorique de la [email protected]

MS105

Application of First-Passage Ideas to the Statisticsof Lead Changes in Basketball

We investigate occurrences of lead changes in NBA basket-ball games. For evenly-matched teams, so that the scoredifference can be modeled as unbiased diffusion, the proba-bility P(t) that a lead change occurs at time t in a game oflength T is exactly soluble and surprisingly has maxima att=0 and t=T. We generalize to teams of unequal strengthsand also provide a criterion for when a lead of a given sizeis safe.

Sidney RednerBoston UniversityPhysics [email protected]

Aaron ClausetUniversity of Colorado at BoulderComputer [email protected]

Marina KoganUniversity of ColoradoComputer [email protected]

MS106

Bifurcation Analysis of a Model for the El NinoSouthern Oscillation

We consider a phenomenological model for the El NinoSouthern Oscillation system in the form of a delay-differential-equation. We conduct a bifurcation analysisof the model in the two parameters of seasonal forcingstrength and oceanic wave delay time, dividing the param-eter plane into regions of different solution types. Our anal-ysis highlights parameter sensitivity, explains and expandson previously published results and uncovers surprisinglycomplicated behaviour concerning the interplay betweenseasonal forcing and delay-induced dynamics.

Andrew KeaneDepartment of MathematicsThe University of [email protected]

Bernd KrauskopfUniversity of AucklandDepartment of [email protected]

Claire PostlethwaiteUniversity of [email protected]

MS106

Interplay of Adaptive Topology and Time Delay inthe Control of Cluster Synchronization

We suggest an adaptive control scheme for the control ofzero-lag and cluster synchronization in delay-coupled net-works. Based on the speed gradient method, our scheme

192 DS15 Abstracts

adapts the topology of a network such that the target stateis realized. The emerging topology is characterized by adelicate interplay of excitatory and inhibitory links leadingto the stabilization of the desired cluster state. As a cru-cial parameter determining this interplay we identify thedelay time. Furthermore, we show how to construct net-works such that they exhibit not only a given cluster statebut also with a given frequency. We apply our method tocoupled Stuart-Landau oscillators, a paradigmatic normalform that naturally arises in an expansion of systems closeto a Hopf bifurcation. The successful and robust control ofthis generic model opens up possible applications in a widerange of systems in physics, chemistry, technology, and lifescience.

Judith LehnertInstitut fur Theoretische PhysikTechnische Universitat [email protected]

Alexander FradkovDepartment of Theoretical CyberneticsSaint-Petersburg State [email protected]

Eckehard Scholl, Philipp HovelInstitut fur Theoretische PhysikTechnische Universitat [email protected], [email protected]

Anton SelivanovDepartment of Theoretical CyberneticsSaint-Petersburg State [email protected]

MS106

Connection Between Extended Time-DelayedFeedback and Nonlinear Fixed-Point Problems

Time-delayed feedback control is an elegant method to findperiodic orbits in an experiment without a-priori knowl-edge of their shape. However, the method has varioustopological restrictions, limiting the cases where it can beused. This presentation will use a singular perturbationargument to show that for the extended time-delayed con-trol (as introduced by Socolar) the classical odd-numberlimitation still holds in the limit of slow updating of thereference signal.

Jan SieberUniversity of [email protected]

MS106

Pattern Formation in Systems with Multiple De-layed Feedbacks

Dynamical systems with complex delayed interactions arisecommonly when propagation times are significant, yieldingcomplicated oscillatory instabilities. We consider systemswith multiple, hierarchically long time delays, and using asuitable space-time representation we uncover features oth-erwise hidden in their temporal dynamics. The behavior inthe case of two delays is shown to ’encode’ two-dimensionalspiral defects and defects turbulence. A multiple scale anal-ysis sets the equivalence to a complex Ginzburg-Landauequation. We also demonstrate this phenomenon for a

semiconductor laser with two delayed optical feedbacks.

Serhiy YanchukHumboldt University of [email protected]

MS107

Voltage Stability in Power Networks and Micro-grids

The AC power flow equations in a complex network displaya rich phenomenology, but despite more than four decadesof investigation the solution space remains poorly under-stood. Here we present a sharp and intuitive parametriccondition for the existence of a stable power flow solution.Our condition immediately leads to non-conservative load-ing margins, grid stability indices, and an accurate seriesexpansion of the stable solution. We illustrate our resultswith monitoring and control applications.

Florian DorflerMechanical EngineeringUniversity of California at Santa [email protected]

John Simpson-PorcoUniversity of [email protected]

Francesco BulloMechanical & Environmental EngineeringUniversity of California at Santa [email protected]

MS107

Finding Useful Statistical Indicators of Instabilityin Stochastically Forced Power Systems

Via a case study of a multi-machine power system, we iden-tify those (relatively few) system variables whose measuredautocorrelation and variance provide reliable warning of in-stability sufficiently before a collapse occurs. Our searchfor such useful early warning signs (EWS) is enabled by asemi-analytical calculation based on the Lyapunov equa-tion and is confirmed by simulations. We also study howthese statistics are impacted by measurement noise anddiscuss methods to reduce that impact. Several numericalexperiments confirm the validity of the identified EWSsand also reveal potential limitations.

Goodarz Ghanavati, Paul HinesUniversity of [email protected], [email protected]

Taras LakobaUniversity of VermontDepartment of Mathematics and [email protected]

MS107

A Parametric Investigation of Rotor Angle Stabil-ity Using Direct Methods

An estimate of the critical clearing time (CCT) for a fault isformulated using the direct methods for power system tran-sient stability. By perturbing the energy functions used inthe direct methods we present an analytic stability metricthat can be used as a lower bound for the CCT. This new

DS15 Abstracts 193

metric is used to support a parametric enquiry into thestability of a small but non-trivial power system.

Lewis G. RobertsUniversity of Bristol (UK)[email protected]


Mario Di BernardoUniversity of BristolDept of Engineering [email protected]

Keith BellUniversity of StrathclydeGlasgow, [email protected]

MS107

Synchronization Stability of Lossy and UncertainPower Grids

Direct energy methods have been extensively developed forthe transient stability analysis and contingency screening ofpower grids. However, there are no analytical energy func-tions proposed for power grids with losses. The difficultyoriginates from the nonlinear and asymmetric couplingsamong generators, which make the natural energy functionnondecreasing. This paper extends the recently introducedLyapunov Functions Family method to certify the synchro-nization stability for lossy multimachine power grids. Wepresent techniques to explicitly construct Lyapunov func-tions and propose algorithms for Lyapunov function adap-tation to specific initial states, both by solving a numberof linear matrix inequalities (LMIs). The Lyapunov Func-tions Family approach is also applicable to uncertain powergrids where the stable equilibrium is unknown due to possi-ble uncertainties in the mechanical torques. We formulatethis new control problem and introduce techniques to cer-tify the robust stability of a given initial state with respectto a set of equilibria.

Konstantin TuritsynMassachusetts Institute of [email protected]

Thanh Long [email protected]

MS108

Bifurcations of Generalised Julia Sets Near theComplex Quadratic Family

We consider a nonanalytic perturbation of the complexquadratic family that is associated to wild Lorenz-likechaos. The perturbation opens up the critical value toa disk and saddle points and their stable and unstable setsappear. These sets interact with the generalised Julia set,leading to the (dis)appearance of chaotic attractors andto generalised Julia sets in the form of Cantor bouquets,Cantor tangles and Cantor cheeses.

Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. OsingaUniversity of AucklandDepartment of Mathematics

[email protected],[email protected], [email protected]

MS108

A Global Bifurcation of Mixed-mode Oscillations

This talk describes the existence of an elusive Shilnikov bi-furcation in the Koper model. This result closes a chapterin one of the early and influential investigations of com-plex and chaotic mixed-mode oscillations. The bifurcationis located using a mixture of investigations of invariantmanifold intersections and continuation methods. We alsostudy structural stability and global returns, leading us toformulate a modified geometric model for a Shilnikov bi-furcation in the slow-fast regime.

Ian M. LizarragaCornell Center for Applied [email protected]

John GuckenheimerCornell [email protected]

MS108

Parameterization Method for Local Sta-ble/unstable Manifolds of Periodic Orbits

I will discuss a numerical method for computing sta-ble/unstable manifolds of periodic orbits for differentialequations that leads to high order Fourier-Taylor expan-sions for the invariant manifolds. The inputs are Fourierseries approximations of the periodic orbit and its Floquetnormal form which are computed using iterative algorithmsand Galerkin projections. The Fourier approximation ofthe Floquet normal form is then used in order to efficientlycompute the parameterization of the local invariant mani-fold.

Jason Mireles JamesRutgers [email protected]

MS108

Practical Stability Versus Diffusion in the SpatialRestricted Three-body Problem

We examine the role of the four-dimensional centre man-ifold W c

L3of the equilibrium L3 of the Spatial Restricted

Three-Body Problem, and its stable and unstable invari-ant manifolds, in two dynamical processes for a small massparameter. The first one consists of the Arnold diffusionmechanism associated to the existence of transition chainsof heteroclinic connections. The second process consists oflong-term confinement of trajectories in a practical stabil-ity domain in a large vicinity of L4,5.

Maisa O. TerraITA - Technological Institute of AeronauticsMathematics [email protected]

Carles SimoUniversity of [email protected]

Priscilla de Sousa-SilvaInstituto Tecnologico de Aeronautica, Brazil

194 DS15 Abstracts

[email protected]

MS109

Perspectives on Theories of Diabetogenesis andGlucose Management

The personalization of treatment is a key difficulty in theclinical management of type 2 diabetes today. Althoughit is widely agreed that glucose control is central to anti-diabetic therapy, there is little consensus on how to achieveit. We believe that the concurrent measurement of redoxstatus, such as through glutathione in particular, can beused to assess the progress of therapy as well as providequantitative targets for glucose control. In my talk I willdescribe reasons in support of this argument, and a mini-mal model for achieving it. I will also present a theory ofdiabetogenesis that implicates oxidative stress as a centralcausal factor, and our attempts at modeling it.

Pranay GoelIndian Institute for Science Education and [email protected]

Saroj GhaskadbiDept. of ZoologySavitribai Phule Pune [email protected]

MS109

Therapeutic Mechanisms of High FrequencyDBS in Parkinsons Disease: Neural RestorationThrough Loop-Based Reinforcement

High frequency deep brain stimulation (HFS) is clinicallyrecognized to treat parkinsonian movement disorders butits mechanisms remain elusive. Current hypotheses sug-gest that the therapeutic merit of HFS stems from increas-ing the regularity of the firing patterns in the basal gan-glia (BG). Although this is consistent with experimentsin humans and animal models of Parkinsonism, it is un-clear how the pattern regularization would originate fromHFS. To address this question, we built a computationalmodel of the cortico-BG-thalamo-cortical loop in normaland parkinsonian conditions. We simulated the effectsof subthalamic deep brain stimulation both proximally tothe stimulation site and distally through orthodromic andantidromic mechanisms for several stimulation frequencies(20-180Hz) and, correspondingly, we studied the evolutionof the firing patterns in the loop. The model closely repro-duced experimental evidence for each structure in the loopand showed that neither the proximal effects nor the dis-tal effects individually account for the observed patternchanges, while the combined impact of these effects in-creases with the stimulation frequency and becomes signifi-cant for HFS. Perturbations evoked proximally and distallypropagate along the loop, rendezvous in the striatum, and,for HFS, positively overlap (reinforcement), thus causinglarger post-stimulus activation and more regular patternsin striatum. Reinforcement is maximal for the clinically-relevant 130Hz stimulation and restores a more normal ac-tivity in the nuclei downstream. These results suggest thatreinforcement may be pivotal to achieve pattern regular-ization and restore the neural activity in the nuclei down-stream, and may stem from frequency-selective resonantproperties of the loop.

Sridevi SarmaJohns Hopkins [email protected]

Sabato SantanielloUniversity of [email protected]

MS109

Unification of Neuronal Spikes, Seizures, andSpreading Depression

The pathological phenomena of seizures and spreading de-pression have long been considered separate physiologicalevents in the brain. By incorporating conservation of par-ticles and charge, and accounting for the energy required torestore ionic gradients, we extend the classic HodgkinHux-ley formalism to uncover a unification of neuronal mem-brane dynamics. By examining the dynamics as a functionof potassium and oxygen, we now account for a wide rangeof neuronal activities, from spikes to seizures, spreadingdepression (whether high potassium or hypoxia induced),mixed seizure and spreading depression states, and theterminal anoxic wave of death. Such a unified frameworkdemonstrates that all of these dynamics lie along a con-tinuum of the repertoire of the neuron membrane. Ourresults demonstrate that unified frameworks for neuronaldynamics are feasible, can be achieved using existing bio-logical structures and universal physical conservation prin-ciples, and may be of substantial importance in enablingour understanding of brain activity and in the control ofpathological states.

Steven J. SchiffPenn State UniversityCenter for Neural [email protected]

Yina WeiUniv California [email protected]

Ghanim UllahUniversity of South [email protected]

MS109

Termination of Cardiac Alternans Using IsostableResponse Curves

Phase reduction has been tremendously useful for under-standing the dynamics of nonlinear oscillators, but hasbeen difficult to extend to systems with stable fixed points,such as excitable systems. Using the notion of isostables,we present a general method for isostable reduction of ex-citable systems. This reduction is applied to both single-and multi-cell systems of cardiac activity in order to for-mulate an energy optimal control strategy to terminatecardiac alternans, a precursor to cardiac arrest.

Dan D. WilsonMechanical EngineeringUniversity of California, Santa [email protected]

Jeff MoehlisDept. of Mechanical EngineeringUniversity of California – Santa [email protected]

MS110

Triggers of Rogue Waves in Deep Water Envelope

DS15 Abstracts 195

Equations

Rogue ocean waves have caused considerable damage toships and coastal structures. We analyze the role of spa-tial localization in triggering rogue waves in the modifiednonlinear Schrodinger equation. Specifically, we develop areduced order model that allows us to determine the char-acteristics of wave packets likely to focus and grow in am-plitude. We use this analysis to develop a computationallyefficient scheme for predicting rogue waves by identifyingthese potentially dangerous wave packets.

Will [email protected]

Themistoklis SapsisMassachusetts Institute of [email protected]

MS110

Boundary Conditions and the Linking of Compu-tational Domains in Patch Dynamics Schemes


I. G. KevrekidisPrinceton [email protected]

MS110

Resilient Algorithms for Reconstructing and Sim-ulating Gappy Flow Fields in CFD

It is anticipated that in future generations of massivelyparallel computer systems a significant portion of proces-sors may suffer from hardware or software faults renderinglarge-scale computations useless. In this work we addressthis problem from the algorithmic side, proposing resilientalgorithms that can recover from such faults irrespectiveof their fault origin. In particular, we set the foundationsof a new class of algorithms that will combine numericalapproximations with machine learning methods.

Seungjoon LeeDivision of Applied Mathematics, Brown Universityseungjoon [email protected]

Ioannis KevrekedisPrinceton [email protected]

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge [email protected]

MS110

Better Buffers for Patches in Macroscale Simula-tion of Systems with Microscale Randomness

The ‘equation-free’ methodology couples many smallpatches of microscale computations across space to em-power computational simulation over macroscale spatialdomains of interest. We derive generally optimum cou-pling of patches and core averaging when the microscale isinherently ‘rough’ as in molecular or agent simulations. Asa canonical problem in this universality class we analyse the

case of inhomogeneous diffusion on a lattice. The minimalerror on the macroscale is generally obtained by couplingpatches with patch cores half as large as the patch, thuscreating coupling active over the other half of the patch.The results indicate that patch dynamics is useful for com-putational simulation of a wide range of systems with finescale roughness.

Anthony J. RobertsUniversity of [email protected]

MS111

Controlling Hyperbolic Trajectories and InvariantManifolds in Flows

Hyperbolic trajectories are important in governing fluidmotion, since their attached stable and unstable manifoldsform crucial flow separators. We derive the control veloc-ity ensuring that a hyperbolic trajectory follows specifiednonautonomous motion in IRn. We control both the Lorenzsystem, and a 3D droplet model, respectively obtaininga specified long-term attractor, and intra-droplet mixing.Ongoing work on determining control velocities for obtain-ing prescribed nonautonomous (un)stable manifold motionis also presented.

Sanjeeva BalasuriyaUniversity of AdelaideSchool of Mathematical [email protected]

Kathrin Padberg-GehleInstitute of Scientific ComputingTU [email protected]

MS111

Closed-Loop Control of Complex and TurbulentFlows Using Machine Learning Control: a ReverseEngineering Approach

We propose a model-free methodology to find closed-loopcontrol laws for complex and turbulent flows using geneticprogramming. Avoiding the necessity to derive a model,the sensor-to-control law is derived by creating and evolv-ing expression-trees according to a cost function. We showthe efficiency of the method by the control of strongly non-linear systems, and its practicality by exhibiting the resultsobtained on four turbulent experimental flows.

Thomas DuriezBuenos Aires UniversityLaboratory of Fluid [email protected]

Vladimir Parezanovic, Kai Von Krbek, Jean-Paul Bonnet,Laurent CordierInstitute PPRIME, [email protected],[email protected],[email protected],[email protected]

Bernd R. NoackInstitut PPRIME, [email protected]

Marc Segond, Markus W Abel

196 DS15 Abstracts

Ambrosys [email protected], [email protected]

Nicolas Gautier, Jean-Luc AiderPMMH Laboratory, UMR 7636 CNRS, [email protected], [email protected]

Cedric Raibaudo, Christophe Cuvier, Michel StanislasLaboratoire de Mecanique de Lille, UMR CNRS 8107Ecole Centrale de [email protected], [email protected],[email protected]

Antoine Debien, Nicolas Mazellier, Azeddine KourtaLabratoire PRISME, Universite d’Orleans, Orleans,[email protected],[email protected],[email protected]

Steven BruntonUniversity of [email protected]

MS111

Mesohyperbolicity, Mix-Norm and the Hunt forMh370

The disappearance of MH370 has exposed the disconcert-ing lack of efficient methods for searching objects movingin a complex and dynamic environment. Lagrangian kine-matics of mesoscale features are visible in mesohyperbolic-ity maps which can be used to predict the time evolution ofany initial distribution and incorporated in the design of asearch strategy. A modified version of DSMC search algo-rithm determines multiple search agents trajectories usingergodicity ideas and the Mix-Norm as a metric.

Sophie LoireUniversity of California Santa [email protected]

Hassan ArbabiUC Santa [email protected]

Stefan IvicRijeka [email protected]

Patrick [email protected]

Bojan Crnkovic, Nelida Crnjaric-ZicRijeka [email protected], [email protected]

Igor [email protected]

MS111

Control of Thin-Layer Flows with Patterned Sur-faces

When a shallow layer of inviscid fluid flows over a

smoothly-patterned substrate, the fluid particle trajecto-ries are, to leading order in the layer thickness, geodesics onthe two-dimensional curved space of the substrate. We use3D-printed substrates to show that the pattern made by ajet striking a bumpy surface is described by the geodesicequation. Because the geodesic equation is fourth order,the geodesics are chaotic even for simple substrates. Thiscould offer a new method of improving mixing by varyingthe shape of the substrate.

Jean-Luc ThiffeaultDept. of MathematicsUniversity of Wisconsin - [email protected]

Jay JohnsonUniversity of Texas at [email protected]

MS112

Experimental Observation of Rhythm Control ofHuman Gait Using Moving Floor

Human and animals maintain stability of gait and postureby tuning their motion rhythms. In order to approach thisrhythm control mechanisms, human motion with floor dis-turbance is measured and rhythm characteristic of humanis discussed. Response to high frequency floor disturbanceduring walking is observed for calculating the phase re-sponse curve, and response to rotational floor is measuredfor considering the posture control.

Tetsuro FunatoMechanical EngineeringJapanese University of [email protected]

Shinya Aoi, Nozomi Tomita, Tsuchiya KazuoKyoto Universityshinya [email protected], [email protected], [email protected]

MS112

What Can Coupled, Nonlinear Oscillators SayAbout Noisy, Perturbed Cockroaches

Cockroaches are remarkably stable runners, exhibitingrapid recovery from external perturbations. To uncoverthe mechanisms responsible for this, we recorded leg kine-matics of freely running animals in both undisturbed andperturbed trials. Perturbations were applied to single legsvia magnetic impulses and the resulting transient effectson all legs and recovery times to normal pre-perturbationkinematics were studied. We estimated coupling architec-tures and strengths by fitting data to a six leg-unit phaseoscillator model. Using maximum likelihood techniques,we found that a network with nearest-neighbor interlegcoupling best fitted the data, and that, while couplingstrengths vary among preparations, overall inputs enter-ing each leg are approximately balanced and consistent.Simulations of models encountering perturbations suggestthat the coupling schemes estimated from our experimentsallow animals relatively fast and uniform recoveries fromperturbations. This is joint work with E. Couzin-Fuchs, T.Kiemel, O. Gal and A. Ayali.

Philip HolmesPrinceton UniversityProgram in Applied and Computaional Mathematics &

DS15 Abstracts 197

MAE [email protected]

MS112

Formation Mechanism for Basin of Attraction ofBipedal Working Models

In this presentation, I will talk about the stability of simplebipedal walking models. Especially, I focus on the geomet-ric structure of basin of attraction. By some numericalcomputations for the basin of attraction, interesting andcomplex geometric structures, for example, the region isthin and fractal-like, but the formation mechanism is notknown. I will explain the mechanism with the saddle prop-erty and hybridness of bipedal walking models.

Obayashi IppeiDepartment of MatheamticsKyoto [email protected]

MS112

Lateral Balance of Human Walking and HumanStructure Interaction

Although synchronisation of pedestrian frequencies to lat-eral ground vibrations has been observed in the past, themechanism leading to this behaviour is still not well un-derstood. To this end experimental data from pedestriansfreely-walking on a laterally oscillating treadmill are anal-ysed revealing adaptive stepping patterns. At the sametime simple spring-mass models of this motion are derivedand analysed. The applicability of Kuramoto synchronisa-tion model to capture this behaviour is examined.

John MacdonaldCivil Engineering DepartmentUniversity of [email protected]

Jeremy BurnUniversity of [email protected]¿

Matteusz BocianUniversity of ExeterUniversity of [email protected]


MS113

The Evolution of Complexity in Arctic Melt Ponds:a Statistical Physics Perspective

Recent analysis of Arctic melt pond images reveals thatthe pond shape transitions from simple to complex arounda critical area of 100 square meters. To explain this on-set of complexity, a two-dimensional Ising model for pondevolution is proposed that incorporates ice-albedo feedbackand the underlying thermodynamics. A second-order phasetransition from isolated to clustered ponds is found, withthe pond complexity in the clustered phase consistent withthe observations.

Yiping Ma

Department of Applied MathematicsUniversity of Colorado, [email protected]

MS113

Statistical Physics Models for Critical Phenomenain Permafrost Lakes

There is an interesting problem, where geometrical changesof the patterns and its stochastic behavior can lead to thecritical phenomena in a climate system. As a result of tun-dra permafrost thawing, permafrost lakes have extended,and methane from ground has entered the atmosphere. Wehave suggested a nonlinear model for phase transitions inpermafrost lakes (based on Ginzburg-Landau theory fromstatistical physics). We have applied this model to studyabrupt permafrost methane emission.

Ivan SudakovUniversity of UtahMathematics [email protected]

MS113

Growth and Fluctuations of Suncups on AlpineSnowpacks: Comparison of Field Observationswith a Nonlinear Pde Model

A mathematical model for suncups on alpine snow exposedto solar radiation is compared with field observations. Themodel consists of a fourth order nonlinear partial differ-ential equation similar to the KPZ equation. The pat-terns fluctuate chaotically in time, and the fluctuations canbe described in terms of diffusion of individual suncups.The rate at which the suncups diffuse contains informa-tion about the effect of the suncups on the albedo of thesnow.

Tom TiedjeFaculty of EngineeringUniversity of [email protected]

Kevin A. MitchellSimon Fraser UniversityDepartment of [email protected]

MS113

How Climate Model Complexity Impacts the Sta-bility of the Sea Ice Cover

Two types of idealized climate models find instabilities dur-ing the retreat of sea ice under global warming: (i) annual-mean latitudinally-varying diffusive energy balance modelsand (ii) seasonally-varying single-column models. Compre-hensive global climate models, however, typically find noinstabilities. To bridge this gap, we develop an idealizedmodel that includes both latitudinal and seasonal varia-tions. Our results suggest that the ice cover is significantlymore stable than found in previous idealized models.

Till WagnerScripps Institution of OceanographyUniversity of California San [email protected]

Ian Eisenman

198 DS15 Abstracts

Scripps Institution of [email protected]

MS114

Possible Mechanisms for Generation of Beta Oscil-lations in Parkinsons Disease

In Parkinson’s disease abnormal oscillations in neural ac-tivity in beta frequency range (13-30Hz) have been ob-served in the basal ganglia, and their power correlates withthe severity of symptoms. We consider a simple model ofcortico-basal-ganglia circuit. We show that there exist dif-ferent regions of its parameters for which the model canmatch the dataset of Tachibana et al. describing neuralactivity in Parkinson’s disease. These different regions cor-respond to different mechanisms of oscillations’ generation.

Alexander PavlidesUniversity of [email protected]


Rafal BogaczAssociate ProfessorOxford University, [email protected]

MS114

Identifying and Tracking Transitions in NeuralSpiking Dynamics in the Subthalamic Nucleus ofParkinsons Patients

Accurate statistical modeling of spiking dynamics in neu-rological disease is important for understanding how thedisease develops, progresses, and manifests clinical symp-toms. In particular, abnormal oscillatory firing patterns ofneurons in the subthalamic nucleus (STN) of patients withParkinson’s disease (PD) have been postulated to play arole in the pathogenesis of motor deficits. We present apoint process analysis framework that allows us to iden-tify and characterize the rhythmic dynamics in STN spiketrains, test for statistically significant changes to those dy-namics, and track the temporal evolution of such changes.The approach incorporates generalized linear modeling the-ory for point processes with state space modeling to esti-mate, instant by instant, changes in the influence of pastspiking history on the current spiking probability. Wedemonstrate the method on both simulated and actual datarecorded from human STN.

Uri EdenAssociate Professor Department of Mathematics andStatisticsBoston [email protected]

MS114

Oscillations and Action Selection in a Multi-Channel Model of the Basal Ganglia

We present a population-level model of basal ganglia actionselection based on segregated oscillatory channels, star-likeconnectivity and partial synchronisation. Although a pair

of STN and GP populations (a ”micro-channel”) cannotoscillate without self-excitation, in pairs they show rhyth-mic activity at a range of intrinsic frequencies, chosen dur-ing training. Adjusting the intrinsic frequency of a centralchannel selects groups of micro-channels via partial syn-chronisation. We describe the analysis and possible bio-logical interpretation of our model.

Roman M. BorisyukSchool of Computing and Mathematics, PlymouthUniversityPL4 8AA, [email protected]

Robert Merrison-HortPlymouth [email protected]

MS114

Cortical Impact on the Dynamics of Subthalamo-pallidal Networks

Parkinsonian hypokinetic motor symptoms are associatedwith the beta-band synchronized oscillations throughoutbasal ganglia-thalamo-cortical circuits. This study ex-plores the oscillatory interactions between cortical andbasal ganglia networks in Parkinson’s disease in the modelof the basal ganglia. The patterns of responses of beta-band bursting in the model suggest that the experimentallyobserved beta-band synchronization in Parkinson’s diseasemay be promoted by the simultaneous action of both cor-tical and subthalamo-pallidal network mechanisms.

Leonid RubchinskyDepartment of Mathematical SciencesIndiana University Purdue University [email protected]

Sungwoo AhnIndiana University Purdue University [email protected]

Elizabeth ZauberIndiana University School of [email protected]

Robert WorthDepartment of NeurosurgeryIndiana University School of [email protected]

MS115

Topology Predicts Dynamics; Dynamics ConstrainTopology

Networks are often the structure on which high dimensionaldynamical systems operate. Inferring network topologyfrom dynamics and constructing networks to exhibit tar-get dynamics are complimentary strategies to understandtheir interplay. Recent efforts can infer the structure of anetwork from manipulations and observations of networkdynamics. A computational study of a detailed model of aneuronal network suggests that networks with similar dy-namics exist in connected sets in the space of all possiblenetworks.

Srinivas Gorur-ShandilyaInterdepartmental Neuroscience ProgramYale University, US

DS15 Abstracts 199

[email protected]

MS115

Data-Driven Network Inference: Achievements,Problems, Possible Research Directions

Complex networks are powerful representations of spatiallyextended systems and can advance our understanding oftheir dynamics. A large number of analysis techniquesis available that aim at inferring the underlying networkstructure from data. Despite great successes in variousfields, there still exist a number of problems for which thereare currently no satisfactory solutions. This talk will dis-cuss these problems as well as possible research directionsto help find better solutions.

Klaus LehnertzDepartment of EpileptologyUniversity of Bonn, [email protected]

MS115

Network Structure from Responses of Time-invariants

Inferring how complex systems are interconnected solelyfrom dynamical experiments [1] constitutes a fundamentalinverse problem with practical relevance across the naturaland technical sciences. So far, most inference approacheseither require a high degree of knowledge about the unitsand the coupling modes or rely on the system being insimple states such as close to fixed points. Moreover, mostapproaches require the knowledge of the temporal order ofthe units’ states or their relations. Here we present a com-plementary approach that instead employs invariant mea-sures (i.e. distributions of points sampled in state space)in response to small driving forces. Given sufficiently longtime series, inference is successful for very distinct systems,from networks of chaotic oscillators to genetic regulatorycircuits underlying the circadian clock. These results ex-pand our ability to infer structural connectivity of networksgiven temporally unordered observations, possibly stem-ming from different experiments with uncontrolled initialconditions. [1] J. Phys. A: Math. Theor. 47:343001 (2014).

Mor NitzanHebrew University of [email protected]

Jose CasadiegoMax Planck Institut for Dynamics and [email protected]

Marc TimmeNetwork Dynamics, Max Planck Inst. f. Dyn. & Self-Org.Goettingen, [email protected]

MS115

Data Based Modelling: Inferring the Direct Di-rected Network Structure from Data

Recent years have seen a large increase in the availabil-ity of data. Increasing amounts of data play a key rolein every aspect of our lives. Dealing with these data setsefficiently determines the success of projects, treatments,assessments, and analyses. This necessity to better un-

derstand and analyze data has led to an outburst of re-search into advanced methods of data based modeling. Weaddress various approaches to network inference based ontime series data.

Bjorn SchelterInstitute for Complex Systems and Mathematical BiologyUniversity of Aberdeen, [email protected]

Marco ThielDepartment of Physics - King’s CollegeUniversity of Aberdeen, [email protected]

MS116

Averaging and Kam Theory in Torus Canards

We consider rotated slow-fast systems of van der Pol type.Depending on the rotation speed, the resulting 3D systemhas 2 fast or 2 slow variables. There exists also an interme-diate region with three timescales. In the region of two fastvariables we prove the existence of an invariant torus andin the intermediate regime we use KAM theory to show theexistence of chaotic dynamics.

Albert GranadosSISYPHE, INRIAalberto.granados [email protected]

MS116

Averaging and Generic Torus Canards

Recently, torus canards have been identified in a rangeof neuronal burster models, and the majority of theseslow/fast systems have a single slow variable. The tran-sition from spiking to bursting occurs via a torus canardexplosion, resulting in the existence of non-generic toruscanards within a small parameter range. We analyse acoupled neuron model with two slow variables, and usingaveraging, identify folded saddle and node singularities.These structures and their bifurcations result in generictorus canards, leading to rich dynamics over a wide pa-rameter range.

Kerry-Lyn RobertsUniversity of [email protected]

MS116

Torus Canard Breakdown

We discuss the conditions giving rise to torus and period-doubling bifurcation pathways from tonic spiking to burst-ing in slow-fast systems typical in life science applications.We employ Poincare return maps to disclose fine details ofthe torus breakdown resulting in the rapid onset of sponta-neous bursting in a Hodgkin-Huxley type model of a haircell. Hair cells are peripheral receptors serving on the firststage in transduction of mechanical stimuli to electricalsignals in the senses of hearing and balance of vertebrates.These sensors rely on nonlinear active processes to achieveastounding sensitivity, selectivity and dynamical range.


200 DS15 Abstracts

Alexander NeimanOhio [email protected]

MS116

The Interaction Between Classical Canards andTorus Canards

Canards are separatrices of slow/fast systems that lie at theintersection of attracting and repelling invariant slow man-ifolds. Closely associated with folded equilibria, canardshave been studied extensively in R

3. Less well-understoodare torus canards, which lie at the intersection of attractingand repelling families of limit cycles. In this work, we ex-plore the relationship between folded node/saddle canardsand torus canards in various model systems.

Theodore VoUniversity of [email protected]

MS117

The Kuramoto Model of Coupled Oscillators with aBi-Harmonic Coupling Function” Maxim Komarov

We study synchronization in a Kuramoto model of glob-ally coupled phase oscillators with a bi-harmonic couplingfunction, in the thermodynamic limit of large populations.We develop a method for an analytic solution of self-consistent equations describing uniformly rotating complexorder parameters, both for single-branch (one possible stateof locked oscillators) and multi-branch (two possible val-ues of locked phases) entrainment. We show that syn-chronous states coexist with the neutrally linearly stableasynchronous regime. The latter has a finite life time forfinite ensembles, this time grows with the ensemble size asa power law.

Maxim KomarovDepartment of Physics and AstronomyPotsdam [email protected]

MS117

On the Mechanical Origin of Chimera States

Previously, we have demonstrated the emergence ofchimera states in an experiment with mechanical oscilla-tors (Martens, E. A., et al. PNAS (2013)) and introduceda mathemtical model based on mechanical principles. Here,I analyze this model and establish a link to abstract math-ematical models in which chimera were originally discov-ered. With the analysis, I explain the stability diagram,discuss a new state and provide the first physical interpre-tation of how chimeras may arise in real world situations.

Erik A. MartensMax Planck Institute for Dynamics & [email protected]

MS117

Chimera States in Globally Coupled Oscillators

Chimera states in coupled oscillator systems, where despiteof full symmetry, part of the oscillators are synchronizedwhile other are desynchronized, have attracted large inter-est recently, also because of several experimental realiza-

tions. Probably, the most nontrivial situation is that of aglobally coupled populations, where one and the same forceacts on all oscillators in the ensemble. We give two exam-ples of chimera formation in such a setup, and describe theunderlying mechanisms of sel-induced bistability betweensynchrony and asynchrony.

Arkady PikovskyDepartment of PhysicsUniversity of Potsdam, [email protected]

Michael RosenblumPotsdam UniversityDepartment of Physics and [email protected]

Azamat YeldesbayDepartment of Physics and AstronomyUniversity of Potsdam, [email protected]

MS117

Mean Field Theory of Assortative Networks ofPhase Oscillators

In this talk I present a technique to study synchronizationin large networks of coupled oscillators, combining a meanfield approximation with the ansatz of Ott and Anton-sen. The formulation is illustrated on a network Kuramotoproblem with degree assortativity and correlation betweenthe node degrees and the natural oscillation frequencies.We find that degree assortativity can induce transitionsfrom a steady macroscopic state to a temporally oscillatingmacroscopic state through Hopf and SNIPER bifurcations.

Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]

Edward OttUniversity of MarylandInst. for Research in Electronics and Applied [email protected]

MS118

Singular Bogdanov-Takens Bifurcations in thePlane

We present perturbations from planar vector fields having aline of zeros and representing a singular limit of Bogdanov-Takens (BT) bifurcations. We introduce the notion ofslow-fast BT-bifurcation and we provide an overview of acomplete study of the bifurcation diagram and the relatedphase portraits, based on geometric singular perturbationtheory, including blow-up.

Peter De MaesschalckHasselt [email protected]

MS118

Canard Orbits in Planar Slow-Fast Piecewise-Linear Systems

The basis of most neuron models is to assume that a neu-

DS15 Abstracts 201

ron behaves as an electrical circuit, which are faithfullymodeled by piecewise linear (PWL) systems. Also, neuronmodels are characterized by different time scales. In thiswork, we analyze the existence of canard orbits in a familyof planar PWL slow-fast systems. The purpose is to use theresults to provide models of neurons equally efficient to thesmooth models, offering better mathematical tractability.

Soledad Fernandez-GarciaInria [email protected]

Mathieu Desroches, Martin KrupaINRIA [email protected], [email protected]

Antonio E. TeruelUniversity of the Balearic IslandsPalma, [email protected]

MS118

Theoretical Analysis of Homoclinic Canards


Jean-Pierre FrancoiseUniversity Pierre & Marie Curie - Paris [email protected]

MS118

Folded Nodes, Canards and Mixed Mode Oscila-tions in 3D Piecewise-Linear Systems

New advances in 3D piecewise-linear slow-fast systems(PWL) are presented. In particular, a complete compari-son with the smooth case near folded singularities is shown:singular phase portraits, singular weak and strong canardsand control of the number of maximal canards are obtainedin a way that is entirely compatible with the smooth case.Furthermore, by using previous analysis we present a mini-mal model displaying periodic canard induced mixed modeoscillations near a PWL folded-node.

Antonio E. TeruelUniversity of the Balearic IslandsPalma, [email protected]

Mathieu DesrochesINRIA [email protected]

Enrique PonceDepartamento de Matematica AplicadaEEscuela Tecnica Superior de Ingeniera, Seville, [email protected]

Rafel ProhensUniversity of the Balearic Island, Palma [email protected]

Antoni GuillamonPolitecnic University of [email protected]

Emilio FreireDepartamento Matematica Aplicada IIUniversidad de Sevilla, [email protected]

MS119

Symbolic Dynamical Unfolding of Spike-Adding Bi-furcations in Chaotic Neuron Models

We show the systematic changes in the topological struc-ture of chaotic attractors occurring as spike-adding and ho-moclinic bifurcations are encountered in the slow-fast dy-namics of neuron models (detailed in the Hindmarsh-Rosemodel), where we show that the UPOs appearing after eachspike-adding bifurcation are associated with specific sym-bolic sequences opened when the small parameter of thesystem decreases. This allows us to understand how thesebifurcations modify the internal structure of the chaoticattractors.

Roberto BarrioUniversity of Zaragoza, [email protected]

Marc LefrancPhLAM/Universite Lille I,[email protected]

M. Angeles MartinezUniversity of [email protected]

Sergio SerranoUniversity of Zaragoza, [email protected]

MS119

Stokes Phenomenon in a Singularly Perturbed Dif-ferential Equation

It is well known that bifurcation problems can often bestudied with the help of singular perturbation theory. Inthese problems invariant manifolds and solutions can befound in the form of formal series. The series typicallydiverge and relations with analytical solutions is describedby the Stokes phenomenon. In this talk we discuss therecent developments of the theory and illustrate it withexamples.

Vassili GelfreichUniversity of Warwick, [email protected]

MS119

Canard Orbits and Mixed-Mode Oscillations in aChemical Reaction Model

To study how mixed-mode oscillations are organised inKoper’s three-dimensional chemical reaction model, wecompute the two-dimensional attracting and repelling slowmanifolds and their intersection curves, known as canardorbits. We also show how a tangency between the repellingslow manifold and the two-dimensional unstable manifoldof a saddle-focus equilibrium shapes the dynamics locally

202 DS15 Abstracts

and globally.

Bernd Krauskopf, Jose Mujica, Hinke M. OsingaUniversity of AucklandDepartment of [email protected], [email protected],[email protected]

MS119

Homoclinic Orbits With Many Loops Near a 02iωResonant Fixed Point Of Hamiltonian Systems

In this talk we study the existence of homoclinic connec-tions near the equilibrium point of a family of Hamiltoniansystems in the neighborhood of a 02iω resonance. For re-versible non Hamiltonian vector fields, the splitting of thehomoclinic orbits lead to exponentially small terms whichprevent the existence of homoclinic connections with oneloop to periodic orbits of size smaller than an exponentiallysmall critical size. The same phenomenon occurs here butwe get round this difficulty thanks to geometric argumentsspecific to Hamiltonian systems and by studying homo-clinic orbits with many loops.

Tiphaine JezequelLMPT, Universite de [email protected]

Patrick BernardCEREMADE, Universite Paris - [email protected]

ric LombardiInstitut de Mathematiques de ToulouseUniversite Paul Sabatier, Tolouse, [email protected]

MS120

Slow Manifolds for a Nonlocal Spde

This work is concerned with invariant manifolds for aslow-fast nonlocal stochastic evolutionary system quanti-fied with a scale paramenter. Under suitable conditions, itis proved that an invariant manifold exists. Furthermore,it is shown that if the scale paramenter tends to zero, theinvariant manifold tends to a slow manifold which captureslong time dynamics.

Lu BaiHuazhong University of Science and [email protected]

MS120

Slow Manifolds and Interface Motion for StochasticPDEs

We consider examples of spatially one-dimensional stochas-tic partial differential equations like the Cahn-Hilliardequation perturbed by additive noise, and study the dy-namics of interfaces for the stochastic model. The dynamicof the stochastic infinite dimensional system is given bythe motion along a finite dimensional deterministic slowmanifold M parametrized by the interface positions. Mainresults include stochastic stability for M , and a derivationof an effective equation for the interface positions. Jointwork with Dimitra Antonopoulou and Georgia Karali.

Dirk Blomker

Universitat [email protected]

MS120

On the Complete Dynamical Behavior for ThreeDimensional Stochastic Competitive Lotka-VolterraSystems


Jifa JiangShanghai Normal [email protected]

MS120

Self-similarity in Stochastic PDEs

This talk present some methods to study the self-similarityof some SPDEs under certain assumptions. Attraction ofthe self-similar solution is shown by applying random in-variant manifold theory (in almost sure sense) and a diffu-sion approximation (in distribution) in the case of additivenoise and stochastic advection respectively.

Wei WangNanjing [email protected]

MS121

Exploring Experimental Paths for Reliable Mathe-matical Models of Friction

Structural vibration controlled by interfacial friction iswidespread, ranging from earthquakes and violin strings,to vehicle brake squeal and friction dampers in gas tur-bines. To predict, control or prevent these systems’ be-haviours, a constitutive description of frictional interac-tions is inevitably required. We shall explore the validityof friction models from the nonlinear dynamics of a drivenforced single degree of freedom oscillator in view of recentexperimental data gathered from the Cambridge pin-on-disc experiment.

Thibaut PutelatUniversity of [email protected]

MS121

Testing of a Spacecraft Structure with Non-SmoothNonlinearities

The dynamics of the SmallSat, a real-life spacecraft pos-sessing a complex isolation device with multiple nonsmoothnonlinearities, is investigated. Experiments show that non-linearities induce modal interactions between modes withnon-commensurate linear frequencies. A model of thestructure with a simplified description of the nonlinear con-nections is first built using techniques available in indus-try. Numerical continuation is then exploited to computenonlinear normal modes and uncover the interaction phe-nomena which can jeopardize the structural integrity.

Ludovic RensonUniversite de [email protected]

J.P. Noel, G. Kerschen

DS15 Abstracts 203

University of [email protected], [email protected]

MS121

Painleve Paradox: Lessons That We Do Not Learnfrom Simple Examples

Painleve's paradox (non-uniqueness and non-existence inthe dynamics of rigid multi-body system with friction) isusually studied via single-contact examples, which exhibita limited variety of interesting dynamics. In this talk, Ishow new phenomena based on the analysis of systems withtwo unilateral, sliding contacts. These include seeminglyregular systems, which fail to follow a unique and existingsolution; and systems, in which the lack of solutions is notresolved by 'tangential impacts'.

Peter L. VarkonyiBudapest University of Technology and [email protected]

MS121

Nonlinear Dynamics and Bifurcations of Rotor-Stator Contact in Rotating Machines

A modified Jeffcott rotor model is studied that includes theeffects of coupled lateral-torsional deformations and rotor-stator contact with friction. Numerically, bifurcations arefound that cause instability or lift-off of either forward orbackward whirl. The results are compared for three differ-ent nonsmooth friction laws and are favorably comparedwith analytical predictions. Implications of the results forthe dynamics of drill-strings and turbomachinery are dis-cussed.

Nicholas VlajicQuantum Measurement Division: Force and Mass GroupNational Institute of Standards and [email protected]


Michael Friswell, Kiran VijayanSwansea [email protected], [email protected]

MS122

Nonlinear Waves in a Lugiato-Lefever Model

The Lugiato-Lefever equation is a cubic nonlinearSchrodinger equation with damping, detuning and driv-ing force arising as a model in nonlinear optics. Steadywaves of this equation are found as solutions of a four-dimensional reversible dynamical system in which the evo-lutionary variable is the space variable. Relying upon toolsfrom bifurcation theory and normal forms theory, we showthe existence of various types of steady solutions, includ-ing spatially localized and periodic solutions. Finally, wediscuss some stability properties of periodic solutions.

Mariana HaragusUniversite de Franche-Comte

[email protected]

MS122

Stability of Traveling Waves in a Model for a ThinLiquid Film Flow

We consider a model for the flow of a thin liquid film downan inclined plane in the presence of a surfactant, which isknown to possess various families of traveling waves. Weuse a combination of analytical and numerical means toshow that the spectra of these waves are within the closedleft-half complex plane.

Vahagn ManukianMiami University [email protected]

MS122

Oscillons Near Hopf Bifurcations of Planar Reac-tion Diffusion Equations

Oscillons are planar, spatially localized, temporally os-cillating, radially symmetric structures often arising nearforced Hopf bifurcations.Using spatial dynamics, we showthat the dynamics on the center manifold of a periodicallyforced reaction diffusion equation (fRD) near a Hopf bi-furcation can be captured by the forced complex Ginzbur-gLandau equation (fCGL). Thus, oscillon solutions to thefRD can be thought of as a foliation over localized solutionsto the fCGL.

Kelly McquighanBoston [email protected]


MS122

The Entry-exit Function and Geometric SingularPerturbation Theory

For small ε > 0, the system x = ε, z = h(x, z)z, withh(x, 0) < 0 for x < 0 and h(x, 0) > 0 for x > 0, ad-mits solutions that approach the x-axis while x < 0 andare repelled from it when x > 0. The limiting attractionand repulsion points are given by the well-known entry-exitfunction. For h(x, z)z replaced by h(x, z)z2, we explain thisphenomenon using geometric singular perturbation theory.The linear case can be reduced to the quadratic case, whichis related to periodic traveling waves in a diffusive predator-prey model.

Peter De MaesschalckHasselt [email protected]

Stephen SchecterNorth Carolina State UniversityDepartment of [email protected]

MS123

Pattern-formation in Semiarid Vegetation: Using

204 DS15 Abstracts

Bifurcation Theory for Model Comparison

In semi-arid ecosystems, water is considered a limiting re-source for vegetation growth. This principle gives rise toa variety of PDE models describing vegetation-water in-teractions that predict the formation of self-organized spa-tial patterns in vegetation communities as a response toresource scarcity. We use bifurcation theory to identify ro-bust structures that persist across different models of thisphenomenon. From this perspective, we find system behav-iors that are robust to uncertainty in model choice, and weidentify models that are not sensitive to small structuralperturbations.

Sarah IamsNorthwestern UniversityEvanston, [email protected]

MS123

Models of Patchy Invasion: A Mathematical ToyOr a New Paradigm?

A theory based on diffusion-reaction equations predicts theinvasive species spread as a traveling population front sep-arating the invaded and non-invaded regions. However, itappears to be at odds with some recent observations. Insome cases, the spread takes place through formation ofa distinct patchy spatial structure without any continuousboundary. I will revisit the traditional diffusion-reactionframework and show that the patchy spread is its inherentproperty in case the invasive species is affected by predationor pathogens. The patchy spread described by a diffusion-reaction model appears to be a scenario of alien speciesinvasion ”at the edge of extinction”. I will also show thatpatchy spread is not an exclusive property of the diffusion-reaction systems but can be observed as well in differenttypes of model.

Sergei PetrovskiiDepartment of MathematicsUniversity of [email protected]

MS123

The Effect of Slow Spatial Processes in aPhytoplankton-Nutrient Model

We consider a system of reaction-diffusion equations de-scribing the interaction of phytoplankton in the deep oceanwith its nutrient. Recently, we have studied bifurcationsand stability of two types of patterns exhibited by thisPDE system. The result is two-fold. On the one hand,our analysis captures field observations, thereby validat-ing the model we used. On the other hand, our analysisis of mathematical interest. In a formal derivation, usingasymptotic methods, we extend a classic version of centermanifold reduction to a regime where the, usually neces-sary, spectral gap condition is violated. With this tool, wecapture parameter regimes in which each of the patterns isstable and flourishes.

Lotte SewaltLeiden [email protected]


Antonios ZagarisUniversiteit [email protected]

MS123

Stripe Pattern Selection by Advective RD Systems:Resilience of Banded Vegetation on Slopes

We study a Gray-Scott type system of PDEs that modelsvegetation in (semi-)arid regions. Observations of stripepatterns along slope contours are widespread. We focuson stripe break up into rectangles/hexagons. It is shownthat an increase in slope/advection leads to an increaseof resilience/stability of vegetation stripes. The analyticalresults generalize to classes of systems.

Eric SieroLeiden University, Mathematical [email protected]



MS124

Input-Ouptut Analysis in Channel Flows and Im-plications for Flow Control

The Navier-Stokes equations for channel flows are a pro-totype model for turbulent boundary layer flow control,specifically for the problem of skin-friction drag reduction.To carry out model-based control designs, control-orienteddynamical models of the processes to be controlled areneeded. Such models need to contain the phenomena thatare to be controlled and stabilized. We present an input-output analysis of channel flows, and control-oriented lin-earized models that contain much of the phenomenology ofbypass transition.

Bassam A. BamiehUC Santa [email protected]

MS124

Nematic Liquid Crystal Flow in a Microfluid:Topological Transitions

Motivated by recent experimental work by Sengupta andco-workers on flow of a nematic liquid crystal (NLC) withina microfluidic, we consider flow of NLC within a channel,with homeotropic (perpendicular) anchoring on the direc-tor field at the walls. We find that this setup admits twoexact steady solutions, with distinct director topology; andthat based on energetic arguments, as the flow rate is in-creased, there is a transition from one solution to the other.

Linda CummingsDepartment of Mathematical SciencesNew Jersey Institute of [email protected]

Thomas AndersonCaltech

DS15 Abstracts 205

[email protected]

Lou KondicDepartment of Mathematical Sciences, NJITUniversity Heights, Newark, NJ [email protected]

MS124

Correlating Dynamical Structures with Forcing in2D Flow

Lagrangian Coherent Structures (LCSs) have been widelystudied in recent years, and have been shown to be a usefulcharacterization of complex fluid flows. However, currentmethods to detect LCSs require knowledge of future in-formation, and it is not known how to generate LCSs ondemand. As a step toward moving past simple observa-tion, I will discuss the correlations between forcing in anexperimental quasi-2D flow and the resulting LCSs.

Nicholas T. OuelletteYale UniversityDepartment of Mechanical Engineering and [email protected]

MS124

Multi-Objective Optimal Control of Transport andMixing in Fluids

Aspects of controlling transport and mixing in fluid flowshave received considerable scientific interest in the last fewyears. Here we describe a multi-objective optimal con-trol framework for the optimization of advective processeswith respect to certain transport or mixing properties. Wedemonstrate it with a number of example systems, whichmay serve as simple models of microfluidic devices.

Kathrin Padberg-GehleInstitute of Scientific ComputingTU [email protected]

Sina Ober-BlobaumUniversity of [email protected]

MS126

Effects of Implementing Contraction to Calcium-Voltage Models

In this study we present a systematical methodology toincorporate a contraction model (Negroni Lascano 1996)into fourteen well known single cell electrophysiology (EP)models. To evaluate how well these coupled electrome-chanical (EM) models behave, we study them under pos-textrasystolic pacing (PESP) protocol. We first comparethe dynamics between the new EM models and the originalEP models then we compare the contractile strength of thenew EM models with the experiment (Yue et al 1985).

Yanyan Ji, Flavio M. FentonGeorgia Institute of [email protected], [email protected]

Richard GrayU.S. Food and Drug Administration

[email protected]

MS126

Synchronization of Calcium Sparks and Waves

In this presentation, we show how membrane potential af-fects Ca sparks and waves, especially during delayed af-terdepolarizations (DADs). We use a physiologically de-tailed mathematical model to investigate individual factorswhich affect Ca spark generation and wave propagation.We found that depolarization promotes Ca wave propaga-tion and hyperpolarization prevents it. We will discuss thedetails of the underlying mechanisms in the talk.

Daisuke SatoUC [email protected]

MS126

Nucleation and Dynamics of Spontaneous CaWaves in Cardiac Cells

Spontaneous Calcium release (SCR) occurs when ion chan-nel fluctuations lead to the nucleation of calcium waves incardiac cells. This phenomenon is important since it hasbeen linked to various cardiac arrhythmias. However, todate it is not understood what determines the timing andlocation of the spontaneous events within cells. Here wehave developed a simplified model of SCR and analyzeda determinstic mean field limit sheds light on the essen-tial features of this phenomenon. We find that SCR istypically nucleated at preferred sites of the cell which candetermined by studying the structure of eigenvectors of aclass of Euclidean random matrices. Using this approachwe estimate the timing of SCR in terms of physiological pa-rameters such as the spatial arangement of calcium releaseunits, and the local ion channel kinetics.

Yohannes ShiferawCalifornia State [email protected]

MS126

Complex Dynamic Patterns of Voltage and Cal-cium in Mammalian Hearts

Cardiac dynamics is govern with bidirectional coupling be-tween transmembrane-voltage (Vm) and free intracellularcalcium (Cai). Altering this coupling it is known to bethe important precursor of different forms of cardiac ar-rhythmia and cardiac alternans as triggers for cardiac reen-try. We present our experimental method for simultaneousmeasurements of Vm and Cai with a single sensor, andobtained experimental results of alternans and ventricu-lar fibrillation development in different mammalian hearts(pig, rabbit, cat).

Ilija Uzelac, Flavio M. FentonGeorgia Institute of [email protected],[email protected]

MS127

Dynamic Information Routing in Complex Net-

206 DS15 Abstracts

works


Christoph KirstCenter for Studies in Physics and BiologyRockefeller University, [email protected]

MS127

Unraveling Network Topology from Derivative-Variable Correlations

A method of network reconstruction from the dynami-cal time series is introduced, relying on the concept ofderivative-variable correlation. Using a tunable observableas a parameter, the reconstruction of any network withknown interaction functions is formulated via simple ma-trix equation. We suggest a procedure aimed at optimizingthe reconstruction from the time series of length compara-ble to the characteristic dynamical time scale. Our methodalso provides a reliable precision estimate. We illustrate themethod’s implementation via elementary dynamical mod-els, and demonstrate its robustness to both model and ob-servation errors.

Zoran LevnajicLaboratory of Data TechnologiesFaculty of Information Studies, Novo Mesto, [email protected]

MS127

Reconstructing Network Connectivity by TripletAnalysis

We discuss recovery of the directional connectivity of asmall oscillator network via the phase dynamics reconstruc-tion from multivariate data. Instead of the pairwise anal-ysis, we analyse triplets of nodes and reveal an effectivephase connectivity which is close but generally not equiva-lent to a structural one. By comparing the coupling func-tions reconstructed from all possible triplets, we achieve agood separation between existing and non-existing connec-tions, and thus reliably reproduce the network structure.

Michael RosenblumPotsdam UniversityDepartment of Physics and [email protected]

MS127

From Neural Dynamics to Network Properties andCognitive Function

It remains unclear to what extend structural and functionalnetwork measurements are complementary, or rather pro-vide orthogonal information about network state. We de-veloped framework to capture neuronal correlations overshort timescales and use them to quantify large-scale func-tional connectivity shifts indicative of slower structural net-work changes. We applied it to simulated as well as exper-imental data. We observed state dependent, network-widestructural modifications and significant changes in networkstability, which is linked to behavior.

Daniel MaruyamaDepartment of PhysicsUniversity of Michigan

[email protected]

Nicollette OgnjanovskiDepartment of Molecular, Cellular and DevelopmentalBiologyUniversity of [email protected]

Sara Aton2Department of Molecular, Cellular and DevelopmentalBiologyUniversity of [email protected]

Michal ZochowskiDepartment of Physics and Biophysics ProgramUniversity of [email protected]

MS128

Rigorous Numerics for Symbolic Dynamics andTopological Entropy Bounds

Outer approximations of continuous, discrete-time sys-tems, or maps, incorporate bounded error and allow forthe rigorous extraction of dynamics via Conley Index the-ory and other tools. Recent advances, including joint workwith W. Kalies, M. D. LaMar, R. Trevino and R. Frongillo,have extended the class of maps to which these methodsmay be applied and improved the types of results that onemay obtain, specifically in terms of semi-conjugate sym-bolic dynamics and associated lower bounds on topologicalentropy. I will describe some of this recent work and showsample results.

Sarah DayThe College of William and [email protected]

Rafael FrongilloThe University of California at [email protected]

MS128

Orbital Stability Investigations for TravellingWaves in a Nonlinearly Supported Beam

We consider the fourth-order problem

ϕtt + ϕxxxx + f(ϕ) = 0, (x, t) ∈ R×R+,

with a nonlinearity f vanishing at 0. Solitary waves ϕ =u(x+ ct) satisfy the ODE

u′′′′ + c2u′′ + f(u) = 0 on R,

and for the case f(u) = eu − 1, the existence of at least 36travelling waves was proved in [Breuer, Horak, McKenna,Plum, Journal of Differential Equations 224 (2006)] bycomputer assisted means. We investigate the orbital sta-bility of these solutions via computation of their Morseindicies, which heavily relies on spectral bounds for the lin-earized operator, and using results from [Grillakis, Shatah,Strauss, Journal of Functional Analysis 74 (1987) and 94(1990)]. We make use of both analytical and computer-assisted techniques.

Michael PlumKarlsruhe University (KIT)

DS15 Abstracts 207

[email protected]

MS128

The Parametrization Method in Infinite Dimen-sions

Understanding the dynamics near the equilibrium solutionsof a PDE is a first step towards a global dynamical scaf-fold. Their (un)stable manifolds are a powerful tool in thisanalysis. We apply the Parameterization Method of Cabre,Fontich and de la Llave in order to study finite dimensionalunstable manifolds in infinite dimensional phase space. Wepresent both numerical implementations for some dissipa-tive PDEs and a-posteriori theorems which provide rigor-ous error bounds for the numerical approximations.

Christian P. ReinhardtDepartment of Mathematics, VU University [email protected]

Jason Mireles-JamesDepartement of MathematicsFlorida Atlantic [email protected]

MS128

Rigorous Numerics for Some Pattern FormationProblems

This talk is about applications of recently developed tech-niques from rigorous computational dynamics to patternformation phenomena. We discuss the differences and sim-ilarities in the analytic setup of three examples, namelyradially symmetric spots in the Swift-Hohenberg model,transitions between hexagonal spots and stripe patterns,and phase separation in diblock copolymers. These exam-ples, which entail both ODEs and PDEs, also showcase theinterplay between rigorous numerical methods and asymp-totic techniques.

Jan Bouwe Van Den BergVU University AmsterdamDepartment of [email protected]

MS129

Neural Field Models Which Include Gap Junctions

Neural field models are normally derived under the assump-tion that connections between neurons are synaptic ratherthan via gap junctions. I will show how to derive a neuralfield model from a network of “theta neurons” with bothsynaptic and gap junction connectivity. The derivation isexact in the limit of an infinite number of neurons.

Carlo R. LaingMassey [email protected]

MS129

From Ensembles of Pulse-Coupled Oscillators toFiring-Rate Models

Ensembles of pulse-coupled oscillators are often encoun-tered in biological and technological systems. We report

on two recent findings: 1) The solution of the prototyp-ical model proposed by Winfree in 1967. Using the Ott-Antonsen ansatz, the effect of pulse width on the onsetof macroscopic synchronization is clarified. 2) For ensem-bles of quadratic integrate-and-fire neurons, a “Lorentzianansatz” permits us to obtain exact low-dimensional firing-rate equations; in contrast to the current heuristic modelsused in neuroscience.

Diego Pazo

Instituto de Fisica de Cantabria (IFCA)Santander, [email protected]

Ernest MontbrioUniversitat Pompeu FabraBarcelona, [email protected]

Alex RoxinCentre de Recerca MatematicaBellaterra (Barcelona), [email protected]

MS129

Suppressing Complex Collective Behavior in a Net-work of Theta Neurons by Synaptic Diversity

A large heterogeneous network of globally coupled thetaneurons can demonstrate a range of collective behaviorfrom simple equilibrium states to a collective rhythmicstate. Other complexity such as multistability, quasi-periodicity, and macroscopic chaos can also occur. In thecurrent work, we introduce heterogeneity in the neuronscoupling strength and we find that synaptic diversity in-creases the robustness of equilibrium states and suppressesthe emergence of the collective rhythmic state and othercomplex network behavior.

Lucas LinThomas Jefferson High School for Science and [email protected]



MS130

Mixed-Mode Bursting Oscillations (MMBOs):Slow Passage Through a Spike-adding Canard Ex-plosion

Mixed-Mode Bursting Oscillations (MMBOs) are solutionsof slow-fast dynamical systems that exhibit both small am-plitude oscillations (SAOs) and bursts consisting of one ormultiple large-amplitude oscillations (LAOs). The nameMMBO is given in analogy to Mixed-Mode Oscillations(MMOs), which consist of alternating SAOs and LAOs,without the LAOs being organized into burst events. I willshow how MMBOs are created naturally in systems thathave a spike-adding bifurcation, or spike-adding mecha-nism, and in which the dynamics of one (or more) of the

208 DS15 Abstracts

slow variables causes the system to pass slowly throughthat bifurcation due to the presence of a folded node.The analysis is carried out for a prototypical fourth-ordersystem of this type, which consists of the third-orderHindmarsh-Rose burster, known to have the spike-addingmechanism, and in which one of the key bifurcation pa-rameters also varies slowly.

Mathieu DesrochesINRIA [email protected]

Tasso J. KaperBoston UniversityDepartment of [email protected]

Martin KrupaINRIA [email protected]

MS130

An Organizing Center for Spatiotemporal Bursting

As the fundamental model of two timescales spatiotempo-ral excitability, FitzHugh-Nagumo model has the interpre-tation of a normal form reduction organized by the hystere-sis singularity. We mimick the analog geometric construc-tion in the universal unfolding of the winged cusp and ob-tain a three timescales model for spatiotemporal excitabil-ity. Bursts and traveling bursts are shown to be the pro-totypical behaviors of the proposed model, in full analogywith the spikes and traveling pulses of FitzHugh-Nagumomodel.

Alessio FranciCambridge [email protected]

Guillaume DrionBrandeis UniversityBrandeis, [email protected]

Rodolphe SepulchreUniversity of CambridgeCambridge, [email protected]

MS130

Three Timescale Phenomena in Coupled Morris-Lecar Equations

Theory for the analysis of systems with two timescales iswell established, but some dynamical phenomena are notcaptured by two timescale models and less is understoodabout how to efficiently study systems with three or moretimescales. Motivated by applications in neural dynamics,we study a pair of Morris-Lecar systems coupled so thatthere are three timescales in the full system. We identifycomplex oscillations that appear to be intrinsically threetimescale phenomena, and use geometric singular pertur-bation theory to explain the mechanisms underlying thesesolutions.

Pingyu NanUniversity of [email protected]

Yangyang WangUniversity of [email protected]

Vivien KirkUniversity of [email protected]


MS130

Averaging, Folded Singularities and Torus Canardsin a Coupled Neuron Model

We consider transitions between various bursting and tonicspiking regimes in a coupled neuron model. Analysis of anaveraged reduced system reveals the critical roles of foldedsingularities and the associated bifurcation scenarios, in-cluding a novel FSN III bifurcation; some of these bifur-cations correspond to torus bifurcations, yielding torus ca-nards, in the full system. We also show that the completeset of bifurcations is captured in a canonical system thatcan be treated analytically.

Kerry-Lyn RobertsUniversity of [email protected]



MS131

Unitary Representations of Diffeomorphisms:Halfway Between Koopmanism and TransferOperator Theory

Koopmanism is derived from a representation of diffeo-morphisms on the space of real valued functions. Dualto this pictures is the Frobenius-Perron operator where adiffeomorphism is represented as a linear operator on den-sities. In this talk we will present a unitary representa-tion of the diffeomorphism group on the Hilbert space ofhalf-densities. The resulting representation induces numer-ical advection schemes which will be useful in a variety ofscenarios. In particular, we may create spectral methodswhich preserve the ring structure of functions, conservetotal mass, deform vector fields, and more. Such struc-ture preservation is important as one considers problemsin higher dimensions and requests qualitative accuracy inexchange for numerical precision.

Henry O. JacobsImperial College [email protected]

MS131

Optimal Control Design and Value Function Esti-

DS15 Abstracts 209

mation for Nonlinear Dynamical Systems

This presentation considers the infinite-time discountedoptimal control problem for continuous time input-affinepolynomial dynamical systems subject to polynomial stateand box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of this problem obtainedby first lifting the original problem into the space of mea-sures with continuous densities and then restricting thesedensities to polynomials. These approximations are tight-enings, rather than relaxations, of the original problemand provide a sequence of rational controllers with valuefunctions associated to these controllers converging (undersome technical assumptions) to the value function of theoriginal problem.

Milan KordaEcole Polytechnique Federale de [email protected]

MS131

Transfer Operator Methods for Stability Analysisand Control

Linear transfer Perron-Frobenius operator-based methodsare developed for global stability analysis and control de-sign of deterministic and stochastic nonlinear systems. Thetransfer operator-based Lyapunov measure is introducedas a new tool to verify weaker set-theoretic notion of al-most everywhere stability. Just as an invariant measureis a counterpart of the attractor (recurrence), this mea-sure is demonstrated as a stochastic counterpart of stabil-ity (transience). The Lyapunov measure is shown to bedual to the Lyapunov function. In addition to the theo-retical results, we also present a computational method forthe approximation of the Lyapunov measure and almosteverywhere stabilizing feedback controller. These compu-tational methods are based on set-oriented numerical ap-proaches. The linear nature of the framework provides lin-ear programming-based computational methods for finitedimensional approximation of the Lyapunov measure andstabilizing controller.

Umesh VaidyaIowa State [email protected]

MS131

Numerical Advection of Probability Densities forHigh Dimensional Systems

Understanding the effect of propagating uncertainty in ini-tial condition through dynamical systems is critical whileengineering verifiably safe systems. Given its importance,many numerical methods have been proposed to advectprobability densities over an initial condition set by care-fully manipulating nonnegative valued functions and densi-ties. This management of nonegative objects unfortunatelyrestricts the applicability of these numerical methods tolow dimensional dynamical systems. In this talk, I de-scribe a method to address this shortcoming by developinga linear advection equation over half densities, which canbe thought of as the square root of classical nonnegativedensities. This construction allows us to prove a rate ofconvergence for various numerical methods and allows usto successfully advect smooth probability densities throughhigh dimensional systems.

Ram VasudevanUniversity of California Berkeley

Massachusetts Institute of [email protected]

MS132

Stochastic Center Manifolds Without Gap Condi-tions

The existence of invariant manifolds requires that the spec-trum of linear part of a deterministic system or stochasticsystem contains large gaps. However, for some dynamicalsystems, the condition of spectral gap condition is not sat-isfied. In this case, it is still unknown whether there existsinvariant manifolds. This paper concerns the center man-ifolds of the stochastic systems without the spectral gapcondition.

Xiaopeng ChenPeking [email protected]

MS132

How to Quantify Non-Gaussian Stochastic Dynam-ics?

Dynamical systems arising in engineering and science areoften subject to random fluctuations, which may be Gaus-sian or non-Gaussian described by Brownian motion ora-stable Levy motion, respectively. Non-Gaussianity ofthe noise manifests as nonlocality at a macroscopic level.Stochastic dynamical systems with a-stable Levy motionshave attracted a lot of attention recently. The non-Gaussianity index a is a significant indicator for variousdynamical behaviors. The speaker will present a few as-pects of non-Gaussian stochastic dynamical systems, high-lighting some delicate and profound impact of noise on dy-namics. Then, he will focus on understanding stochasticdynamics by examining certain deterministic quantities.

Jinqiao DuanInstitute for Pure and Applied [email protected]

MS132

Random Dynamical Systems for Non-Densely De-fined Evolution Equations

We consider abstract random evolution equations given by

x′(t) = Ax(t) + F (θtω, x(t)), x(0) = x0 ∈ D(A). (1)

Here, we suppose that A is a non-densely defined linearoperator. Therefore, the C0-semigroup approach no longerapplies. Such situations can occur for instance due to non-linear boundary conditions. By using integrated semigrouptheory, we can show under suitable assumptions, the exis-tence of a random dynamical system for the above equationand discuss its asymptotic behavior. Finally, we analyzea class of non-densely defined stochastic differential equa-tions driven by a Banach-space valued Brownian motion.Our aim is to construct an Ornstein-Uhlenbeck process,which allows us to reduce the stochastic problem into apathwise one.

Alexandra NeamtuFriedrich-Schiller-University Jena

210 DS15 Abstracts

[email protected]

MS133

Lessons Learnt from the Two-Ball Bounce Problem

I revisit a popular classroom demonstration where a lightrigid body and a larger heavier ball are vertically alignedand dropped together. Experimental results obtained us-ing a high-speed camera are compared to a discrete modelusing Newtonian restitution, showing poor agreement asthe separation distance becomes small. An alternativemodel based on membrane theory is developed and com-pared favourably to experimental data in the limits of verysmall separation distance and mass ratio.

Yani BerdeniUniversity of [email protected]

MS133

Predicting Conditions for Self-sustained Vibrationin Drillstrings

High amplitude vibration in drillstrings is often the resultof a self-sustained regime of vibration such as torsionalstick-slip oscillation; forward whirl; or backward whirl.The nonlinear interactions underlying these regimes comefrom bit-rock interaction and side-wall contact. We presenta novel approach for modelling these regimes: assuming lo-cal nonlinearity, we derive conditions necessary to sustain agiven regime once it has already initiated. Results are nu-merically validated and give insight into each phenomenon.

Tore ButlinUniversity of [email protected]

MS133

Contact and Friction Within Geometrically ExactShell Theory - Modeling Microslip and Dissipationin Structural Systems

We consider the representation of the dissipation due tofrictional interfaces within large-scale structural systems.In this work contact and friction are incorporated withingeometrically exact shell theory, providing insight into therelationship between the observed dissipation and the load-ing characteristics on the shell. Finally, the use of suchformulations as a basis for reduced-order modeling and ex-tensions to the larger problem of structural damping arehighlighted.

D Dane QuinnUniversity of AkronDept of Mechanical [email protected]

MS133

A New Semi-Analytical Algorithm for Two-Dimensional Coulomb Frictional System

A closed form solution for the trajectory of a planer par-ticle loaded by constant external force with Coulomb fric-tion has been proposed. Together with analytical patchesclose to slip/stick transitions, this solution has been em-ployed to build a new semi-analytical algorithm for two-dimensional frictional system subjected to time-varying ex-ternal loads under the assumption that the external loads

can be treated as constant if the time step is sufficientsmall.

Xiaosun WangWuhan [email protected]

Jim BarberUniversity of [email protected]

MS134

Stability of Combustion Fronts in HydraulicallyResistant Porous Media

We study front solutions of a system that models combus-tion in porous media. The spectral stability of the fronts isstudied on the linear and nonlinear level. For the spectralstability analysis we use a combination of energy estimatesand numerical Evans function computations.

Anna GhazaryanMiami [email protected]

MS134

Invasion Fronts in Systems of Reaction DiffusionEquations

We study invasion speeds in a system of coupled Fisher-KPP equations. For certain parameter regimes we provethat the speed selected by compactly supported initial datais faster for the coupled system than for the uncoupledone. The proof relies on the construction of sub and supersolutions.

Matt HolzerDepartment of MathematicsGeorge Mason [email protected]

MS134

An Overview of Evans Function Computation

We give an overview of Evans function and the numericaltechniques used to compute it. We provide a mini-tutorialon STABLAB, a MATLAB-based toolbox for Evans func-tion computation, and show how to avoid some of thecommon pitfalls that arise in Evans function computation.There are also a number of best practices that we high-light, noting that there are many variations on methodsand formulations. Different situations call for different ap-proaches.

Jeffrey HumpherysBrigham Young [email protected]

MS134

Orbital Stability of Waves Traveling Along VortexFilaments

By the term vortex filament, we mean a mass of whirlingfluid or air (e.g. a whirlpool or whirlwind) concentratedalong a slender tube. The most spectacular and well-knownexample of a vortex filament is a tornado. A waterspout

DS15 Abstracts 211

and dust devil are other examples. In more technical ap-plications, vortex filaments are seen and used in contextssuch as superfluids and superconductivity. One system ofequations used to describe the dynamics of vortex filamentsis the Vortex Filament Equation (VFE). The VFE is a sys-tem giving the time evolution of the curve around whichthe vorticity is concentrated. In this talk, we develop aframework for studying the stability solutions of the VFE,based on the correspondence between the VFE and theNLS provided by the Hasimoto map. We use this frame-work to establish the orbital stability of certain classes ofsolutions including solitons and closed solutions taking theform of torus knots.

Stephane LafortuneCollege of [email protected]

PP1

The Breakup of Invariant Tori in 4-D Maps Usingthe Slater’s Criterion

In the late of 40s, N. B. Slater proved that an irrationaltranslation over an unity circle can take at most three dif-ferent return counts to a connected interval (δ < 1). In ad-dition, these three recurrence times are expressible by thecontinued fraction expansion of the irrational number usedto the translation. This remarkable result has an immedi-ate connection with invariant tori, whose rotation numberin the bi-dimensional phase space is also irrational and canbe related to a motion over the circle. Thus, the eval-uation of three recurrence times has been used to predictbreakup of such invariant tori in several 2-D dynamical sys-tems. Here we introduce the Slater’s theorem in the con-text of higher dimension Hamiltonian systems to estimatethe breakup of invariant tori in a 4-Dimensional symplecticmap.

Celso AbudUniversity of Sao [email protected]

Ibere L. CaldasInstitute of PhysicsUniversity of Sao [email protected]

PP1

Theta Model for Quartic Integrate-and-Fire Neu-ron Model

The theta model is convenient to investigate the popula-tion dynamics of coupled noisy neurons due to the periodicboundary conditions of the corresponding Fokker-Planckequation. However, quantitative relationships between thetheta model and conductance-based neuron models hasnot been thoroughly explored. We propose a version ofthe theta model derived from a quartic integrate-and-firemodel, which has quantitatively equivalent dynamics tobiophysically realistic Wang-Buzsaki model. We also ana-lyze the population dynamics of this new model.

Akihiko Akao, Yutaro OgawaGraduate School of Frontier SciencesThe University of [email protected],[email protected]

Bard Ermentrout

University of PittsburghDepartment of [email protected]

Yasuhiko JimboGraduate School of EngineeringThe University of [email protected]

Kiyoshi KotaniResearch Center for Advanced Science and TechnologyThe University of [email protected]

PP1

A Solution of Linear Programming Problems withInterval Coefficients

In this talk, we consider a linear programming problemwhere the coefficients are interval. For these problems, wecannot apply the technique of the classical linear program-ming directly. We focus on a satisfactory solution approachbased on the inequality relations that was introduced byAlolyan and to solve the interval linear programming prob-lem. In order to solve such a problem, we present an al-gorithm that find the solution of such a problem and showthe efficiency of the algorithm and present a numerical ex-ample.

Ibraheem AlolyanKing Saud [email protected]

PP1

Developing a Model Approximation Method andParameter Estimates for a Solar ThermochemistryApplication

We will show the model and software development processused in creating a robust parameter optimizer for a solarreactor. The basic reaction model is numerically difficultto solve, so several proprietary elements of code were de-veloped to interface with standard optimization routines.Integrating complex toolboxes and non-standard code ledto several insights into good development practices whichwill be highlighted.

William D. ArloffValparaiso [email protected]

Karl SchmittValparaiso UniversityDepartment of [email protected]

Luke Venstrom, Leandro JaimeValparaiso UniversityDept. of Mechanical [email protected], [email protected]

PP1

Hamiltonian Hopf Bifurcations in SchrdingerTrimers

The cubic nonlinear Schrdinger equation is fundamentallyimportant in the physics of waves, arising in optical fibers,waveguides, Bose-Einstein condensates, and water waves.

212 DS15 Abstracts

We investigate the phase space of the three-mode discreteNLS in the weakly nonlinear regime. We enumerate thefamilies of standing waves and use normal forms to describeseveral families of relative periodic orbits whose topologieschange due to Hamiltonian Hopf bifurcations and others.

Casayndra H. BasarabNew Jersey Institute of [email protected]

Roy [email protected]

PP1

Computing the Optimal Path in Stochastic Dynam-ical Systems

In stochastic systems, we are often interested in quanti-fying the optimal path that maximizes the probability ofswitching between metastable states. However, in high-dimensional systems, the optimal path is often extremelydifficult to approximate. We consider a variety of problemsfrom population biology and demonstrate a constructivemethodology to quantify the optimal path using a com-bination of finite-time Lyaponuv exponents, statistical se-lection criteria, and a Newton-based iterative minimizingscheme.

Martha BauverMontclair State [email protected]



PP1

Effects of Quasi-Steady-State Reduction on Bio-physical Models with Oscillations

Many mathematical models of biological systems possessmultiple time scales. A common first step in the analysisof such models is the elimination of one or more of thefastest variables via quasi-steady-state reduction (QSSR).However, this process sometimes leads to changes in thedynamics by introducing or removing bifurcations. We dis-cuss the persistence of Hopf bifurcations under QSSR andshow examples of qualitative changes to oscillatory dynam-ics that can be induced by QSSR.

Sebastian D. Boie, Vivien KirkUniversity of [email protected], [email protected]

James SneydUniversity of AucklandDepartment of Mathematics

[email protected]

PP1

Analyzing Cycling Dynamics in Stochastic Systems

We consider a Langevin model where external noise causesrandom switching between metastable states. A chain ofthese states, such as those found in a multi-well potential,enables cycling dynamics. Switching times are found us-ing a variational approach. Additionally, a probabilisticargument is used to understand the cycling dynamics. An-alytical results agree well with numerical simulations for arange of well depths and noise intensities.

Pralhad BurliMontclair State [email protected]



PP1

Limit Cycles in a Simplified Basal Ganglia Model

Muscle rigidity associated with Parkinson’s disease isthought to be correlated with the loss of dopamine andthe emergence of beta oscillations in the basal ganglia. Asdopamine-producing neurons die off, synaptic connectionstrengths change leading to a favoring of the Indirect Path-way. Though a model of the entire basal ganglia process isquite complicated, we show that a simplified version can ex-hibit both steady-state and limit cycle behavior by changesin connection strength alone.

Michael CaiolaRensselear Polytechnic [email protected]

Mark HolmesRensselaer Polytechnic [email protected]

PP1

Mathematical Modelling of Spatial Sorting andEvolution in a Host-Parasite System

We examine the spatial self-structuring of traits in both acane toad population and lungworm parasite population,which evolves with the cane toad population. In particular,the traits we focus on are dispersal ability for the cane toadpopulation and both prepatent period and larval size forthe lungworm parasite population. Along with the spatialself-structuring of these traits, our results confirm observa-tions made in empirical studies; particularly, that there isa noticeable lag between the host and parasite population,that older populations regress to lower dispersal speeds andthat “spatial sorting” of dispersal ability can still occurwith a disadvantage in reproductivity and/or survival inmore motile individuals. Moreover, we find that such adisadvantage in reproductivity and/or survival is unlikelyto be large if spatial sorting is to have a noticeable effect

DS15 Abstracts 213

on the rate of range expansion, as it has been observed tohave over the last 60 years in northern Australia.

Matthew H. ChanUniversity of [email protected]

Gregory Brown, Richard ShineSchool of Biological Sciences, University of [email protected], [email protected]

Peter S. KimUniversity of SydneySchool of Mathematics and [email protected]

PP1

Using Tangles to Quantify Topological Mixing ofFluids

Topological entropy (TE), a measure of topological mixing,can be studied by the braiding of ghost rods. We study thesystem of Grover et al. [Chaos 22,043135 (2012)] usinga heteroclinic tangle. In this approach, we explain TEthrough intersecting stable and unstable manifolds usinghomotopic lobe dynamics (HLD). The HLD method usesghost rods placed on heteroclinic orbits, which allows usto compute TE in excess of that given by simple periodicbraiding.

Qianting ChenUniversity of California, [email protected]

Sulimon SattariUniversity of California, MercedSchool of Natural [email protected]


PP1

New Computational Tools for Non-Smooth Dy-namical Systems

We will present development of new computational toolscapable to comprehensively analyse the non-smooth dy-namical systems. They will allow for high accuracy andspeed brute force numerical simulation of dynamical sys-tems having various types of discontinuities. On the sameplatform a powerful and convenient path-following mod-ule is being developed allowing for modelling and analysisof non-smooth systems efficiently. As an example, we willpresent the modelling and analysis of soft impact oscilla-tors. The ultimate aim of the project is to take the state-of-art of computational tools available for non-smooth sys-tems a step further.

Antonio S. ChongCentre of Applied Dynamic Research, CADRUniversity of Aberdeen, Scotland, United [email protected]

Marian WiercigrochCentre for Applied Dynamics Research, School of

Engineering,University of Aberdeen, AB24 3UE, Aberdeen, Scotland,[email protected]

PP1

Modeling the Lymphocytic ChoriomeningitisVirus: Insights into Understanding Its Epidemiol-ogy in the Wild

The lymphocytic choriomenigitis virus (LCMV) is arodent-spread virus commonly recognized as causing neu-rological disease that exhibits asymptomatic pathology.We looked to construct an epidemiological model of amouse population to better understand how this virus canremain endemic. We used an SIRC model that incorpo-rated gender dynamics as to capture the primary aspectsof the disease, and establish some initial findings underwhich the carriers remained stable.

Christy ContrerasArizona State [email protected]

PP1

Causal Relationships Between Time Series: Gener-alizing Takens’ Theorem to a Dynamical Network

We consider a set of scalar time series measured from adynamical system evolving on an invariant manifold M .Takens’ Theorem says that the state space reconstruction(SSR) for a time series is generically diffeomorphic to M .A non-generic SSR does not faithfully represent M . Weprove that it generically represents the dynamics of a feed-back system within the larger dynamical system. Timeseries SSRs are compared to recover potential causal rela-tionships between feedback systems.

Bree CumminsDepartment of MathematicsTulane [email protected]

Tomas GedeonMontana State UniversityDept of Mathematical [email protected]

Kelly SpendloveRutgers [email protected]

PP1

Regular Acceleration from Low Initial Energies ina Magnetized Relativistic System

We consider a relativistic particle interacting with a uni-form magnetic field and a stationary electrostatic wave.According to the parameters of the wave, triangular islandsappear in the low energy region of phase space. In thisscenario, a particle with initial energy close to its rest en-ergy is accelerated and achieves a considerable final energy.We obtain analytically the parameter region for which theparticle can be regularly accelerated from very low initialenergies.

Meirielen C. De SousaInstituto de Fsica, Universidade de So Paulo, Brazil

214 DS15 Abstracts

[email protected]


Fernanda SteffensDeutsches Elektronen-Synchrotron, [email protected]

Renato Pakter, Felipe RizzatoInstituto de Fsica, Universidade Federal Rio Grande [email protected], [email protected]

PP1

Estimating the L∞-Norm of Linear Solutions ofCahn-Hilliard

Using a simple toy model we approach the problem of L∞-bounds on linear solutions of the strong subspace of Cahn-Hilliard solutions and relate it to its pattern development.

Philipp DurenUniversitat [email protected]

PP1

Spike Adding in Transient Dynamics

Many mathematical models of neuron activity exhibit com-plex oscillations in response to stimulus from an appliedcurrent or from other neurons. We consider the effect ofa single short stimulus on a neuron that is otherwise qui-escent, focussing on the transient response induced by thestimulus. We use numerical continuation methods and ex-ploit the presence of different time scales in the model to ex-plain how the oscillatory pattern in the transient responsedepends on parameters.

Saeed FarjamiThe University of [email protected]

Hinke M. OsingaUniversity of AucklandDepartment of [email protected]

Vivien KirkUniversity of [email protected]

PP1

Front-Dynamics and Pattern Selection in the Wakeof Triggered Instabilities

Pattern-forming fronts are often controlled by some ex-ternal stimulus which progresses at fixed speed, renderingthe medium unstable. Such ”triggers” control dynamicsin two generic ways corresponding to pushed and pulledfronts. The former is governed by oscillatory nonlinear in-teractions, leading to hysteresis and multi-stability. Thelatter is governed by absolute spectra and interacts mono-tonically. We use heteroclinic bifurcation and functionalanalytic techniques to study prototypical examples in the

complex Ginzburg Landau and Cahn-Hilliard equations.

Ryan Goh, Arnd ScheelUniversity of [email protected], [email protected]

PP1

Pattern Sequences as Early-warning Signs of Crit-ical Transition in Models of Dryland Vegetation

Regular spatial patterns (resembling tiger stripes and leop-ard spots) occur in the vegetation of many dryland ecosys-tems, and are hypothesized to be a self-organized responseto water scarcity. Numerous partial differential equationmodels of vegetation-water interactions based on this hy-pothesis have been proposed to investigate how patternedecosystems may respond to increased water scarcity. Asa precipitation parameter decreases in value, a sequenceof patterns, gaps → labyrinths → spots, is observed insimulations of many of these models. Observations of thiskind have led this sequence to be suggested as an early-warning sign of dryland vegetation collapse. In a previousbifurcation theoretic analysis, we analytically studied tran-sitions between two pattern-forming instabilities to assessthe generic robustness of the “gaps → labyrinths → spots’sequence. We found that alternative sequences of patternsare possible in this generic setting, and we conjectured thata calculable quantity signals the appearance of the stan-dard pattern transition sequence in the models. Here, wetest this conjecture in two widely studied vegetation modelsthrough weakly nonlinear analyses and numerical simula-tions. We find that our conjecture holds in these modelsfor the space of parameter values considered. In addition,we find that a sequence involving only spot patterns occursas a common alternative to the standard sequence.

Karna V. Gowda, Yuxin ChenNorthwestern [email protected],[email protected]

Sarah IamsNorthwestern UniversityEvanston, [email protected]

Mary SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]

PP1

Rigorous Computation of Radially Symmetric Sta-tionary Solutions of Pdes

We present a rigorous numerical method for proving the ex-istence of radially symmetric solutions of stationary PDEson the entire space. By combining numerical methods withfunctional analytic estimates, we show the existence of asolution by showing the existence of a fixed point of anequivalent fixed-point problem T (x) = x. We shall ap-ply this method to a previously unsolved Ginzburg-Landautype equation.

Chris M. GrootheddeVU University Amsterdam

DS15 Abstracts 215

[email protected]

PP1

Dynamics of Register Transitions in Human VocalFold Modeling

There are several theories as to the mechanism of regis-ter transitions in the human voice. The suddenness ofthe change under smooth variations of aerodynamic andbiomechanical parameters suggests a bifurcation-like phe-nomenon with hysteresis. Often, the mechanics of the hu-man vocal folds are modeled by a simple system of coupledoscillators. We show in theory and simulations what dy-namical phenomena in these systems could generate suchtransitions.

Jesse HaasGIPSA-Lab, Institut Polytechnique de [email protected]

PP1

A Mathematical Model of Saliva Secretion and Cal-cium Dynamics

Oscillations in free intracellular calcium (Ca2+) concen-tration carry signals that control cellular processes such asneuronal firing and secretion. Experimental data show thatoscillations of Ca2+ in certain salivary duct cells are cou-pled to oscillations in inositol trisphosphate (IP3). I willdescribe a recently constructed model of Ca2+ dynamicsin salivary duct cells that captures important dynamicalfeatures of the data and shows how the dynamics of IP3

affects certain features of the calcium oscillations.

Jung Min Han, James Sneyd, Vivien KirkUniversity of [email protected], [email protected],[email protected]

PP1

Mixed-Mode Oscillations and Twin Canards

We consider mixed-mode oscillations (MMOs), featuringa mix of small and large amplitudes, in dynamical sys-tems with one fast and two slow variables. These oscilla-tions are organised by canard orbits, which are intersectioncurves between attracting and repelling two-dimensionalslow manifolds. We show how paired or twin canards withthe same number of small oscillations arise in fold bifur-cations of slow manifolds, and what this implies for theobserved MMOs.

Ragheb HasanUniversity of [email protected]

Hinke M. Osinga, Bernd KrauskopfUniversity of AucklandDepartment of [email protected], [email protected]

PP1

A Dynamical Analysis of Steam Supply NetworkBased on Invariant Manifold

In this presentation, we analyze dynamics of heat supply ina simple steam supply system. The system consists of twosteam boilers and a steam pipe which enables heat transfer

between the two boilers. An invariant manifold represent-ing steady operating condition of the system is located, andits existence and persistence are investigated. This clarifiesthe stability aspect of the steam supply system.

Hikaru HoshinoDepartment of Electrical Engineering, Kyoto [email protected]

Yoshihiko SusukiKyoto University / [email protected]

PP1

Defects in Spatially Extended Systems

We look at the effects of defects on pattern formation asa perturbation problem. We present a few examples ofspatially extended pattern forming systems, and explainwhy regular perturbation theory fails due to critical con-tinuous spectrum. We show how Kondratiev spaces canhelp alleviate this difficulty: the linearization at periodicpatterns becomes a Fredholm operator, albeit with nega-tive index. Together with far-field matching procedures,we obtain deformed stripe patterns or pacemakers usingimplicit function type continuation.

Gabriela JaramilloUniversity of [email protected]

Arnd ScheelUniversity of MinnesotaSchool of [email protected]

PP1

Delayed Feedback Model of Axonal Length Sensing

It has been proposed that an axon is able to gauge itsown length based on the frequency of the oscillations ofa molecular motor-based retrograde chemical signal. Thefrequency is inversely related to the length of the axon.We model the chemical oscillations using a system of delaydifferential equations and reproduce this relationship. Wethen investigate the behavior of these chemical signals aswe model motor dynamics using stochastic partial differ-ential equations.

Bhargav R. KaramchedUniversity of UtahSalt Lake City, [email protected]


PP1

Nonlinear Dynamical Systems in Finance

Dynamical system is very popular and important issue intodays World. It is important to understand systems ingeology, mathematics, microbiology, biology, computer sci-ence, economics, engineering, finance, algorithmic trading,meteorology, philosophy, physics, politics, population dy-namics, psychology, meteorology, robotics etc. Then with

216 DS15 Abstracts

having clear understanding about system we can make bet-ter predictions. In poster, definition and usage areas ofnonlinear dynamical system and chaos will be covered.Main aim is understanding the dynamical system in fi-nance.

Deniz K. KilicSIAM student membership,student at Middle EastTechnical University,Institute of Applied Mathematics(member ofSIAM)[email protected]

PP1

Polyrhythmic Synchronization in Modular Net-works

CPGs comprised of coupled interneuron circuits underliewide ranges of natural rhythmic behaviors. Phase lagreturn maps describing polyrhythmic behavior in three-node reciprocally-inhibitory Fitzhugh-Nagumo type net-works characterize regimes of robustness and stability sim-ilar to natural patterns. Further, we examine complexrhythm generation in modular network settings couplingtwo such networks. Transition from small local-networks toso-called network-of-networks permits within-circuit multi-phase coordinated pattern storage that may underlie learn-ing and memory of more complex motor rhythm patterns.

Jarod CollensGeorgia State UniversityNeuroscience Institute and Mathematics [email protected]



Drake KnapperGeorgia State [email protected]

PP1

Discriminating Chaotic and Stochastic DynamicsThrough the Permutation Spectrum Test

In this poster a new test for detecting determinism fromtime series data will be presented. The test involves lookingfor reoccurring patterns in time series data. The test willbe described and the results of the test applied to severalmodel systems and real-world data sets will be presented.The presentation will conclude with a discussion of futureavenues of research related to the test.

Christopher W. KulpDept. of Physics and [email protected]

Luciano ZuninoCentro de Investigaciones pticas (CONICET LaPlata-CIC)

[email protected] ¡[email protected].

PP1

Coupling Methods As a Tool for Sensitivity Anal-ysis of Stochastic Differential Equations

Under appropriate assumptions of Ergodicity, the expectedvalue of observables for dynamical systems can be approx-imated by time averages. The introduction of stochas-tic forcing in the form of additive white noise can resultin greatly increased varience of the observable estimates,making sensitivity analysis a delicate task. In this setting,coupling methods can be employed as a tool for varience re-duction. The methods and their applications to StochasticDifferential Equations will be discussed.

Andrew LeachUniversity of [email protected]

PP1

Transient Dynamics in Ensemble of InhibitoryCoupled Rulkov Maps

We study numerically three Rulkov maps with mutual in-ertia inhibitory couplings. We study numerically differentdynamical regimes that can be obtained in this ensembleby governing coupling parameters, in particular, sequen-tial activity regime and multistable regime, and bifurcationtransition from one regime to another.

Tatiana A. Levanova, Grigory OsipovLobachevsky State University of Nizhny [email protected], [email protected]

PP1

Complex Collective Behavior in a Network ofTheta Neurons is Suppressed by Synaptic Diver-sity

In the wake of a study that examined the collective dy-namics of a large network of uniformly coupled Type 1neurons, we explored how the patterns of macroscopic be-havior change with respect to alterations in different neu-ron parameters of a model that includes realistic biologi-cal diversity through connection variability. Our analysisdemonstrated that heterogeneity in coupling strength in-creases the robustness of equilibrium states and increasingsynaptic diversity suppresses the emergence of the collec-tive rhythmic state.

Lucas LinThomas Jefferson High School for Science and [email protected]



PP1

Shape Coherence and Finite-Time Curvature Evo-

DS15 Abstracts 217

lution in Time-Dependent Dynamical Systems

We present finite-time curvature (FTC) as a local propen-sity of curvature elements to change. The FTC simplifiesthe recent study of shape coherence in nonautonomous dy-namical systems. Trough (low) FTC curves indicate shapecoherent sets. Finding slowly evolving boundary curvaturedescribes slowly changing shapes in otherwise complex non-linear flows, where stretching and folding may dominate.FTC troughs are often nearby the popular Finite-TimeLyapunov Exponent (FTLE) ridges, but often the FTCindicates entirely different regions.

Tian MaDepartment of Mathematics and Computer ScienceClarkson [email protected]


PP1

Snaking on Networks: From Local Solutions toTuring Patterns

The emergence of patterns of activity on complex networkswith reaction-diffusion dynamics on the nodes is studied.The transition is investigated between the single-node so-lutions, studied previously [Wolfrum, Physica D (2012)],and the fully developed global activation states (so calledTuring states). Numerical continuation reveals snaking bi-furcations connecting different solutions, similar to thosefound in reaction diffusion systems on regular lattice net-work topologies, shedding light on the origin of the mul-tistable “Turing’ patterns reported previously [Nakao &Mikhailov, Nature 2010].

Nick McCullenArchitecture and Civil EngineeringUniversity of [email protected]

Matthias WolfrumWeierstrass Institute for Applied Analysis and [email protected]

Thomas WagenknechtUniversity of Leedsdeceased

PP1

Fractal Boundaries in the Parameters Space of De-terministic Dynamical Systems

Nonlinear dynamical systems may exhibit sensitivity tosmall perturbations in their control parameters. Such sen-sitivity is source of uncertainties on the predictability oftunning parameters that lead these systems to either achaotic or a periodic behavior. In this work, by quantifyingsuch uncertainties in different classes of nonlinear systems,we obtain the exterior dimension of parameters sets thatlead the system to chaotic or to periodic behavior. we showthat this dimension is fractal, explaining the sensitivityobserved in tunning the parameter to those two behaviors.Moreover, we show that this dimension is roughly the samefor the classes of investigated systems.

Everton S. Medeiros

Physics Institute - University of So [email protected]


Murilo BaptistaUniversity of [email protected]

PP1

A Biophysical Model for the Role of NetworkTopology in Regulating a Two-Phase BreathingRhythm

Respiration occurs in a two-phase pattern, with alternat-ing inspiration and expiration. This arises from alternat-ing activity among groups of neurons in the pre-Btzingerand Btzinger areas in the brainstem. However, much aboutthe network mechanisms that produce this activity remainsunknown. Using a biophysical computational model to ex-plore different topological structures and their ability togenerate a two-phase rhythm, we show how modular vs.random structure of the inhibitory connections affect globaldynamics.

Joshua MendozaDepartment of Applied Mathematics, University ofWashingtonLewis Hall #202, Box 353925, Seattle, WA [email protected]

Kameron Decker HarrisDepartment of Applied Mathematics, University [email protected]

Eric Shea-BrownUniversity of WashingtonDepartment of Applied [email protected]

Jan RamirezCenter for Integrative Brain Research, Seattle [email protected]

Tatiana DashevskiyCenter for Integrative Brain ResearchSeattle Children’s Research [email protected]

PP1

Modeling Effects of Drugs of Abuse on Hiv-SpecificAntibody Responses

Drugs of abuse enhance HIV replication and diminish hostimmune responses. Here, we present a dynamical systemmodel that helps quantify the effects of drugs of abuse onaltering HIV-specific antibody responses. Our model isconsistent with the experimental data from simian immun-odeficiency virus infection of morphine-addicted macaques.Using our model, we show how altered antibody responsesdue to drugs of abuse affect steady state viral load andCD4 count in HIV-infected drug abusers.

Jones M. Mutua

218 DS15 Abstracts

University of Missouri - Kansas City (UMKC)[email protected]

Anil KumarUniversity of Missouri - Kansas [email protected]


PP1

Time-Delayed Model of Immune Response inPlants

When studying the dynamics of plant infections, it is essen-tial to correctly account for detailed mechanisms of plantimmune response. We have developed and analysed a newmathematical model of plant immune response that takespost-transcriptional gene silencing into account. We haveperformed analytical and numerical bifurcation analysisto investigate how stability of the steady states dependson time delays, and also to illustrate different dynamicalregimes that can be exhibited by the model.

Giannis Neofytou, Konstantin BlyussUniversity of [email protected], [email protected]

PP1

Analysis and Control of Pre-Extinction Dynamicsin Stochastic Populations

We consider a stochastic population model where the in-trinsic noise causes random switching between metastablestates before the population goes extinct. Switching andextinction times are found using a master equation ap-proach and a WKB approximation. In addition, a proba-bilistic argument is used to understand the pre-extinctioncycling dynamics. We also implement a control method todecrease the mean time to extinction. Analytical resultsagree well with numerical Monte Carlo simulations.

Garrett NiedduMontclair State [email protected]



PP1

An Explicit Formula for R0 of Tick-Borne Relaps-ing Fever

Tick Borne Relapsing Fever (TBRF) is a disease spreadamong mammals by soft bodied ticks in the WesternUnited States which is characterized by (possibly multiple)relapsing states of fever and muscle aches. There is a nat-ural question regarding how the number of relapse states

affects the spread. In this poster we will use analyticalmethods to derive an expression for TBRF’s fundamentalreproductive number R0 as a function of the number ofrelapses.

Cody PalmerUniversity of [email protected]

PP1

Title Not Available

Our work builds on Kurebayashi et al. (2013), wherethey derive a general phase equation for an autonomoussystem with a slowly varying parameter. We reproducetheir result using the Fredholm alternative, and extend itto weakly coupled oscillators by deriving an equation forthe interaction function with a slowly varying parameter.We test our theory with a lambda-omega system and aTraub+adaptation model using stochastic, periodic, andquasi-periodic slow parameters.

Youngmin ParkUniversity of [email protected]

PP1

Stochastic Motion of Bumps in Planar NeuralFields

We analyze the effects of spatiotemporal noise on station-ary pulse solutions (bumps) in neural field equations onplanar domains. Fluctuations in neural activity are mod-eled as a Langevin equation. Noise causes bumps to wan-der diffusively. We derive effective equations describing thebump dynamics as Brownian motion in two-dimensions.We also consider weak external inputs that can pin thebump so that it obeys an Ornstein-Uhlenbeck process withcoefficients determined by input shape.

Daniel PollUniversity of HoustonDepartment of [email protected]


PP1

Automatically Proving Periodic Solutions to Poly-nomial ODEs

Rigorously proving the existence of a solution to ODEs ina neighborhood of a given numerical approximation is ofprimary importance in order to determine the accuracy ofthe numerical approximation. One approach is to use afunctional analytic setting that is well suited to continu-ation techniques. We discuss an implementation for peri-odic solutions to general systems of polynomial ODEs. Wepresent several examples that serve as test problems for theautomated algorithm.

Elena QueiroloVrije Universiteit Amsterdam

DS15 Abstracts 219

[email protected]

PP1

Repulsive Inhibition Promotes Synchrony in Exci-tatory Networks of Bursting Neurons

We show that the addition of pairwise repulsive inhibitionto excitatory networks of bursting neurons induces syn-chrony, in contrast to one’s expectations. Through sta-bility analysis, we reveal the mechanism underlying thispurely synergetic phenomenon and demonstrate that itoriginates from the transition between bursting of differenttypes, caused by excitatory-inhibitory synaptic coupling.We also reveal a synergetic interplay of repulsive inhibi-tion and electrical coupling in synchronization of burstingnetworks.

Reimbay Reimbayev, Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected], [email protected]

PP1

Quasipatterns in Two and Three Dimensions

Quasipatterns (patterns with no translation symmetry butwith rotation symmetry on average) can occur in a vari-ety of systems, including Faraday waves, nonlinear optics,polymer micelles and coupled reaction-diffusion systems.This poster will explore how having two interacting wave-lengths in the physical system can stabilise quasipatternsin two and three dimensions, or can lead to spatio-temporalchaos.

Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]

PP1

Computing Chaotic Transport Properties in aMixed Phase Space with Periodic Orbits

Chaotic transport can be quantified using periodic orbits,but difficulties arise in a mixed Hamiltonian phase space.Homotopic Lobe Dynamics uses topological forcing by in-tersections of stable and unstable manifolds of anchor or-bits to find periodic orbits in such a space. We computedecay rates for the Henon map in a variety of parameterregimes. In a hyperbolic plateau, periodic orbit continua-tion is used to accurately compute the decay rate for theentire interval.

Sulimon SattariUniversity of California, MercedSchool of Natural [email protected]


PP1

Rigorous Computations for BVPs with Chebyshev-series

The main goal of my research is to bridge the gap between

non-rigorous numerical simulation of dynamical systemsand mathematically sound results. Recently, a rigorousnumerical procedure based on Chebyshev-series (a non-periodic analog of Fourier series) was developed to solveODEs and BVPs. My research is concerned with extend-ing this method by incorporating domain decomposition.Applications include rigorous computations of connectingand periodic orbits in the Lorenz-system.

Ray SheombarsingVU University [email protected]

PP1

Central Configurations of Symmetrically Re-stricted Five-Body Problem

We study the central configuration of a highly symmetricfive-body problem where four of the masses are placed atthe vertices of the isosceles trapezoid and the fifth body cantake various positions on the axis of symmetry. We identifyregions in the phase space where it is possible to choose pos-itive masses which will make the configuration central. Wepropose a global regularization scheme which removes sin-gularities associated with single-binary collisions. Finallywe numerically show existence of quasi-periodic orbits inthe central configuration regions.

Anoop SivasankaranKhalifa University of Science Technology and ResearchDepartment of Applied Mathematics and [email protected]

Muhammad ShoaibUniversity of Hail, Department of MathematicsSaudi [email protected]

Abdulrehman KashifUniversity of Hail, Department of [email protected]

PP1

Finite Time Diagnostics and Transport Barriers inNon Twist Systems

Internal transport barriers that appear in Hamiltonian dy-namical systems have been proposed as an explanation forthe cessation or reduction of transport in physical systemsat describe fluids and plasmas. These barriers may havevarious physical or dynamical origins, yet they can andhave been used to control experiments and sometimes toimprove desired confinement of trajectories. We use theso-called standard nontwist map, a paradigmatic exampleof non twist systems, to analyze the parameter dependenceof the transport through a broken barrier. On varying aproper control parameter, we identify the onset of struc-tures with high stickiness that give rise to an effective bar-riers. We use the finite-time rotation number to identifytransport barriers that separate different regions of stick-iness. The identified barriers are comparable to those ob-tained by using finite-time Lyapunov exponents.

Jose D. Szezech JrUniversity State of Ponta [email protected]

Ibere L. CaldasInstitute of Physics

220 DS15 Abstracts

University of Sao [email protected]

Sergio R. LopesDepartment of PhysicsFederal University of [email protected]


Philip MorrisonPhysics DepartmentUniversity of Texas at [email protected]

PP1

Robust Pulse Generators in An Excitable Medium

We study a spontaneous pulse-generating mechanism in anexcitable medium with jump-type heterogeneity. We in-vestigate the conditions for the onset of robust-type pulsegenerators, and then we show the global bifurcation struc-ture of heterogeneity-induced patterns, including the ho-moclinic orbits that are homoclinic to a special type ofheterogeneity-induced ordered pattern. These numericalapproaches assist us in identifying a candidate for the or-ganizing center as a codimension-two gluing bifurcation.

Takashi TeramotoAsahikawa Medical [email protected]

PP1

Dynamical Building Blocks in Turbulent Two-Dimensional Channel Flow

Although the classical sweep-ejection cycles cannot be self-sustaining itself, two-dimensional channel flows keep themregenerating for a quite long time. The relation betweenlocalized coherent structures and their collective dynamicsis investigated numerically focusing on a turbulent-laminarinterface. The existence of interfaces reduces the complex-ity of the collective dynamics arising around them. Weuse the damping filter technique to simulate a laminar-turbulent interface in a periodic box.

Toshiki TeramuraDepartment of Physics and Astronomy,Graduate School of Science, Kyoto University, [email protected]

Sadayoshi TohGraduate School of Science, Kyoto University, [email protected]

PP1

Phase Models and Oscillators with Time DelayedAll-to-All Coupling

We consider a system modeling a network of globally de-layed coupled identical oscillators. Assuming weak cou-pling, we reduce the system to a phase model where thedelay acts as a phase shift. We show how the delay affects

the stability of different symmetric cluster states, and ap-plied the results to a network of six globally coupled Morris-Lecar oscillators with synaptic coupling. Furthermore, wecompare the phase model results to bifurcation studies ofthe full model.

Zhen WangUniversity of [email protected]

PP1

Efficient Design of Navigable Networks

Navigation is a dynamic process where individual agentstry to reach targets given limited knowledge. In a net-work of agents, we term a successive gradient-like naviga-tion path to the target as a greedy path, and show that(interestingly) it violates many known properties of usualnetwork paths such as symmetry and transitivity even forundirected networks. Despite these complications, we areable to design an efficient scheme that allows every networkto be navigable.

B.M. Shandeepa D. WickramasingheClarkson University, 8 Clarkson avenue, Potsdam,[email protected]

Jie SunClarkson [email protected]

PP1

Instability of Certain Equilibrium Solutions of theEuler Fluid Equations

We look at the stability of the family of stationary solutionscos(mx+ny) of the Euler Equations on a toroidal domain.We use a Poisson structure preserving truncation describedby Zeitlin [1991] to turn the problem into a finite-modesystem, and a splitting into subsystems described by Li[2000]. We show that for many m and n these stationarysolutions are unstable.

Joachim WorthingtonUniversity of Sydney, [email protected]

Holger R. DullinUniversity of SydneySchool of Mathematics and [email protected]

Robby MarangellUniversity of [email protected]

PP1

A Symbolic Method in Chua’s Circuit

A symbolic method is introduced in a three-dimensionalChua’s circuit with a smooth cubic nonlinearity. The newmethod is able to reveal thousands of homoclinic bifurca-tion curves in a bi-parametric plane with a small amount ofcomputational cost. Co-dimension two points, t-points andclose homoclinc curves are detected as well. Based on thebi-parametric plots of the Chua’s circuit, chaotic structure

DS15 Abstracts 221

of the Chua’s circuit is studied.

Tingli XingGeorgia State [email protected]


PP1

Interactions of Solitary Modes in Models of Bacte-rial Chemotaxis

We study the interaction of two colliding bacterial popula-tions in a one-dimensional nutrient gradient. The outcomeof such collisions varies. For example, upon collision, twopopulations of E. coli will either mix together to becomeone indistinguishable population or deflect off and moveaway from one another. We use a Keller-Segel model ofbacterial chemotaxis to determine mechanisms by whicheach observed outcome may occur and make experimentalpredictions about the behavior following a collision.

Glenn S. YoungUniversity of PittsburghDepartment of [email protected]

Hanna SalmanUniversity of PittsburghDepartment of Physics and [email protected]


Jonathan RubinUniversity of PittsburghPittsburgh, [email protected]

PP1

The Spread of Activity with Refractory Periodsover Directed Networks

We study propagation of activity in a discrete time dynami-cal system on several directed network topologies. At eachtime step, active nodes send the signal onward throughtheir outgoing connections, and fall into a refractory pe-riod. In particular, we investigate the number and lengthof attractors (node sequences that can sustain activity in-definitely) and transients on networks of varying topologiesincluding random, small-world, scale-free.

Daniel R. ZavitzUniversity of UtahDepartment of [email protected]

Alla BorisyukUniversity of UtahDept of Mathematics

[email protected]

PP2

Intermittent Synchronization/desynchronizationin Population Dynamics

Synchronous dynamics of spatially distinct oscillating pop-ulations is a well-known phenomenon in ecology. Mathe-matical modeling of this phenomenon has been largely fo-cused on the synchronization conditions and the propertiesof synchronized dynamics. Yet the synchrony in the realpopulations is not necessary strong and therefore exhibitintervals of uncorrelated, desynchronized dynamics. Weexplore the properties of these time-intervals and discusspotential advantages and disadvantages of short numerousdesynchronization intervals vs. few long desynchronizationintervals.

Sungwoo AhnIndiana University Purdue University [email protected]

Leonid RubchinskyDepartment of Mathematical SciencesIndiana University Purdue University [email protected]

PP2

Parabolic Bursting in Inhibitory Neural Circuits

We study the rhythmogenesis of network bursting emergingin inhibitory motifs comprised of tonic spiking interneu-rons described by an adopted Plant model.Such motifs arethe building blocks in larger neural networks, including thecentral pattern generator controlling swim locomotion ofsea slug Melibe leonine.

Deniz AlacamGeorgia State UniversityMathematics [email protected]


PP2

An Accurate Computation of the Tangent Map forComputation of Lagrangian Coherent Structures

The tangent map (flow map gradient) is often used in dy-namical systems for computation of Lagrangian coherentstructures. In more sophisticated methods it is importantto recover the complete spectrum of this operator, as wellas the eigenvectors. Traditional methods to compute thetangent map using finite differencing often fail in accuratelycomputing these quantities. Due to nonlinear effects of theflow, perturbations of trajectories mapped forward by thetangent map may grow excessively and they collapse onthe dominant eigenvector of the map. We describe alter-native techniques to overcome these issues. Both continu-ous or discrete singular value decompositions with efficientimplementations are used to automatically carry out com-putation of finite time Lyapunov exponents and directions.Results on sum of Lyapunov exponents for divergent freeflow, as well as sensitivity to integration time are compared

222 DS15 Abstracts

in contrast to previous methods.

Siavash Ameli, Shawn ShaddenUniversity of California, [email protected], [email protected]

PP2

Nonlinear Dynamics in Coupled SemiconductorLaser Network Implementations

Coupled semiconductor lasers subject to optical injectionand/or feedback are known to exhibit complex dynamicsin their emitted output. Current implementations usuallyemploy only a few lasers in order to map the regimes of theexhibited dynamics. In the present work, a large-scale net-work of coupled semiconductor lasers is built experimen-tally, including up to 24 laser devices. Rich dynamics arerecorded, depending on the conditions of coupling strengthand time delays among the laser nodes.

Apostolos Argyris, Michail Bourmpos, AlexandrosFragkos, Dimitris SyvridisDepartment of Informatics and TelecommunicationsNational & Kapodistrian University Of [email protected], [email protected], alx [email protected],[email protected]

PP2

Symplectic Maps with Reversed Current in a Toka-maks

Plasmas are confined in tokamaks by magnetic field lines.We derive a bidimensional conservative map which de-scribes these lines considering a non-monotonic profile ofsafety factor with reversed current density, first in equilib-rium [C. Martins et al., Analytical solutions for Tokamakequilibria with reversed toroidal current, PoP 18(2011)],and then we will apply a perturbation (ergodic magneticlimiter). We will investigate island chains, chaos and par-ticle transport.

Bruno BartoloniUniversity of Sao PauloInstitute of [email protected]

Ibere L. CaldasInstitute of PhysicsUniversity of Sao [email protected]

PP2

Analysis of Spatiotemporal Dynamical Systemsfrom Multi-Attribute Satellite Images

We deduce and then analyze oceanic fluid systems by re-mote sensing from satellite images. Time varying vec-tor fields are computed from the nonautonomous systemby temporal intensity changes of observed product move-ments. To emphasize prior assumed physics, an objectivefunction and consequent calculus of variations follows. Asan important initial task, we show how to remove sensor-data biased of stripes from images by developing a newapproach in terms of a nonisotropic total variation denois-ing.

Ranil Basnayake, Erik BolltClarkson [email protected], [email protected]

Nicholas TufillaroOregon State [email protected]

Jie SunClarkson [email protected]

PP2

Phase Response Analysis of the Circadian Clock inNeurospora Crassa

Circadian rhythm is crucial in maintaining an organism’sdaily routine. We present a model which accurately sim-ulates the molecular components governing the circadianclock of the model organism, Neurospora crassa. Environ-mental cues such as light perturb the phase of the circadianoscillator, a phenomenon generally measured with a phaseresponse curve (PRC). Our model advocates that Neu-rospora’s phase response to light is primarily regulated bythe degradation of the clock protein White Collar-1 (WC-1).

Jacob BellmanUniversity of [email protected]

PP2

Time Series Based Prediction of Extreme Eventsin High-Dimensional Excitable Systems

We investigate extreme events in a high-dimensional deter-ministic system: a network of FitzHugh-Nagumo units. Wepresent a data-driven approach to predict extreme eventswhich is only based on the time series of some observablesand on the coupling topology of the network. By itera-tive predictions, we are able to forecast the onset of anextreme event as well as the propagation and extinction ofexcitation, i.e. the full life-cycle of an extreme event.

Stephan BialonskiMax-Planck-Institute for the Physics of Complex [email protected]

Gerrit AnsmannDepartment of EpileptologyUniversity of Bonn, [email protected]

Holger KantzMax-Planck-Institute for the Physics of Complex [email protected]

PP2

Slow-fast Analysis of Earthquake Faulting

We consider a rate and state dependent friction law tostudy earthquake fault dynamics. We show that the sys-tem has an embedded slow-fast structure. Using techniquesfrom geometric singular perturbation theory and centremanifold theory we perform an analytical investigation ofthe problem.

Elena BossoliniPh.D. studentDTU Compute, Institute for Mathematics and [email protected]

DS15 Abstracts 223

Kristian Uldall Kristiansen, Morten BrønsTechnical University of DenmarkDepartment of Applied Mathematics and [email protected], [email protected]

PP2

Quasicycles in the Stochastic Hybrid Morris-LecarNeural Model

Intrinsic noise from the stochastic nature of voltage-gatedion channels affects a neuron’s ability to produce sub-threshold oscillations and respond to weak periodic stim-uli. While it is known that stochastic models can produceoscillations in regimes where the deterministic model hasonly a stable fixed point, little work has explored theseconnections to channel noise. Using a stochastic hybridMorris-Lecar model, we use various approximation schemesto derive a stochastic differential equation, then derive thepower spectrum and quantify how oscillations are affectedby channel noise.

Heather A. BrooksUniversity of [email protected]


PP2

Computation of Normally Hyperbolic InvariantManifolds

In this poster we explain a method for the computationof normally hyperbolic invariant manifolds (NHIM) in dis-crete dynamical systems. The method is based in findinga parameterization for the manifold formulating a func-tional equation. We solve the invariance equation usinga Newton-like method taking advantage of the dynamicsand the geometry of the invariant manifold and its invari-ant bundles. Particularly, we present two different kindof methods to compute normally hyperbolic invariant tori,NHIT. The first method is based on a KAM-like theoremin a-posteriori format for the existence of quasi-periodicinvariant tori, which provides us an efficient algorithm forcomputing NHIT, by adjusting parameters of the family.The second method allows us to compute a NHIT and itsinternal dynamics, which is a-priori unknown. We imple-ment both methods to continue the invariant tori with re-spect to parameters, and to explore different mechanismsof breakdown.

Marta CanadellUniversitat de [email protected]

Alex HaroDept. of Mat. Apl. i AnalisiUniv. de [email protected]

PP2

Equivalent Probability Density Moments Deter-mine Equivalent Epidemics in An Sirs Model with

Temporary Immunity

In an SIRS compartment model for a disease we considerthe effect of different probability distributions for remain-ing immune. We show that to first approximation the firstthree moments of the corresponding probability densitiesare sufficient to well describe oscillatory solutions corre-sponding to recurrent epidemics. We consider six differ-ent distributions and show that by tuning their parame-ters such that they have equivalent moments that they allexhibit equivalent dynamical behavior.

Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]

PP2

A Novel Speech-Based Diagnostic Test for Parkin-sons Disease Integrating Machine Learning withWeb and Mobile Application Development forCloud Deployment

Parkinson’s disease remains one of the most poorly diag-nosed neurological conditions despite the critical need ofearly diagnosis for effective management and treatment.This work presents a new method of diagnosing Parkin-son’s disease and accompanying scalable web and mobileapplications towards the goal of employing this diagnostictest to the cloud. This method provides a more simple,inexpensive, and rapid approach than traditional diagno-sis strategies by requiring the patient to only speak intoa microphone attached to their computer or mobile devicebefore providing a diagnosis within seconds. This work em-ploys speech processing algorithms, an artificial neural net-work for machine learning, and an application frameworkwith a user-friendly interface that packages the speech testand diagnosis results for easy access by patients and physi-cians. The diagnosis test developed was tested with actualpatient data and was shown to be highly accurate.

Pooja ChandrashekarThomas Jefferson High School for Science and [email protected]

PP2

An Agent-Based Model for mRNA Localization inFrog Oocytes

During early development of Xenopus laevis oocytes,mRNA moves from the nucleus to the periphery. We usean agent-based model to study the movement of mRNA bymolecular motor transport and diffusion. Our results sug-gest that an anchoring mechanism is required to achieve theobserved localization of mRNA: simulations indicate thatanchoring of a particular motor-mRNA complex may besufficient for relocation and that binding between differentmolecular motors may contribute to transport.

Veronica M. CiocanelBrown UniversityBrown Universityveronica [email protected]

Bjorn SandstedeDivision of Applied MathematicsBrown University

224 DS15 Abstracts

bjorn [email protected]

PP2

Effects of Stochastic Gap-Junctional Coupling inCardiac Cells and Tissue

Action potentials propagate in cardiac tissue in partthrough gap junctions. Gap-junction gating dynamics arefunctions of both gap-junctional voltage and time and alsoare stochastic in nature. We derive a system of stochas-tic differential equations to model these gating dynamicswithin the context of the Luo-Rudy-1 description of ioniccurrents. We perform simulations on a 1D cable and showthe effects of stochastic gating on action potential propaga-tion. Results on conduction block, action potential prop-agation speed and gap junctional resistance will be pre-sented.

William ConsagraRochester Institute of TechnologySchool of Mathematical [email protected]

PP2

Maximizing Plant Fitness Under Herbivore Attack

When attacked by insect herbivores, plants emit volatilechemicals. These chemicals are known to induce local de-fenses, prime neighboring plants for defense, and attractpredators and parasitoids to combat the herbivores, butthese chemical defenses are coupled with fitness costs. Weexamine the interactions between the model plant, gold-enrod, and one of its insect herbivores, Trirhabda virgata,in order to draw conclusions about what defense strategieswill maximize a goldenrods fitness.

Karen M. Cumings, Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected], [email protected]

Bradford C. ListerRensselaer Polytechnic InstituteDepartment of Biological [email protected]

PP2

The Derivation of Mass Action Laws: Issues andQuestions

There are well-trodden paths that enable one to passfrom stochastic individual-based models to deterministicpopulation-level models. I will point out a few issues thatarise along the way: these make the journey slightly moreinvolved and interesting than one might expect.

Jonathan DawesUniversity of [email protected]

Max O. SouzaDepartamento de Matematica AplicadaUniversidade Federal [email protected]

PP2

Heterogeneity and Oscillations in Small Predator-

Prey Swarms

Real-world predator-prey interactions often involve apredator chasing a flock of prey. We examined a dynamicalsystems model of predator-prey interactions, governed byisometric interaction kernels incorporating classical swarm-ing for the prey. Since many parameter values lead to thepredator splitting the swarm into smaller, unevenly-sizedgroups, we investigate the effects of heterogeneity amongpredator-prey interactions in small swarms. We show thata variety of behaviors, including oscillations, are possiblein the small swarm case.

Jeff DunworthUniversity of [email protected]


PP2

Bacterial Disinfection with the Presence of Persis-ters

Many important diseases like Tuberculosis are caused bybiofilms.Among the bacteria within a biofilm, persistersare a subpopulation which are tolerant to antibiotics andknowing more about them is very critical and helpful. Inthis poster we will look at the behavior of the bacteriawith three phases: Susceptible, Stationary and Persisters,and we will show that considering the third phase givesus more accurate results comparing to the previous studieswith just Susceptible and Persisters and this new modelmatches the experimental results better.

Sepideh EbadiFlorida State [email protected]

PP2

Chaotic Mixing in a Curved Channel with Slip Sur-faces

In this work, we show that laminar flow in a planar curvedchannel can generate chaotic trajectories, if the top andbottom walls are alternately patterned with slip surfaces.Existing micro-mixers based on flow through curved sec-tions, have either complex 3D geometries, or are effectiveonly at relatively high Reynolds numbers [Stremler, Phil.Trans. A., 362, 10191036]. Using slip surfaces, we over-come both these limitations, while simultaneously reducingviscous drag on the fluid.

Piyush GargDepartment of Chemical EngineeringIndian Institute of Technology [email protected]

Jason R. Picardo, Subramaniam PushpavanamDepartment of Chemical EngineeringIndian Institute of Technology Madras

DS15 Abstracts 225


PP2

Feasibility of Binding Heteroclinic Networks

Many neuronal systems exhibit multi-sensory dynamics.Multisensory integration is a process by which informationfrom different sensory systems is combined to influence per-ception, decisions, and overt behavior. In this context, thedifferent sensory systems, such as sight, sound, smell, tasteand so on, are called sensory modalities. In each modality,there are cognitive modes which are large collections of neu-rons firing at the same time in synchrony in a functionalnetwork. In order to explain the sequential mental pro-cesses in the brain, we study a heteroclinic binding modelwhere active brain modes form different modalities whichare processed in parallel. Under certain assumptions, theexistence of the so-called multimodality heteroclinic net-work was established. we prove that for each collection ofsuccessive heteroclinic orbits inside the network, there isan open set of initial points such that the trajectory goingthrough each of them follows the prescribed collection ofsuccessive heteroclinic orbits and stays in a small neigh-borhood of it. We also show that the symbolic complexityfunction of the system restricted to this neighborhood isa polynomial of degree L − 1 where L is the number ofmodalities.

Xue GongOhio [email protected]

Valentin AfraimovichUniversidad Autonoma de San Luis PotosS.L.P., [email protected]

PP2

Dynamic Square Patterns in 2D Neural Fields

We present analysis and simulation of periodic solutionsnear D4xT

2 symmetric Hopf bifurcations in two differentneural field models. The first model consists of a scalar in-tegral equation that incorporates finite transmission speedthrough spatiotemporal delays. The second model incorpo-rates finite transmission speed using a telegraph equation(ie. a hyperbolic PDE), but also includes local ion channeldynamics and 2 interacting populations of neurons.

Kevin R. Green, Lennaert van [email protected], [email protected]

PP2

Controllability of Brain Networks

Cognitive function is driven by dynamic interactions be-tween large-scale neural networks, enabling behavior. Weuse control theory to offer a mechanistic explanation forhow the brain moves among cognitive states. Our re-sults suggest that densely connected areas facilitate themovement of the brain to easily-reachable states. Weaklyconnected areas facilitate the movement of the brain todifficult-to-reach states. Areas located on the boundarybetween network communities facilitate the integration orsegregation of diverse cognitive systems.

Shi Gu

Complex Systems GroupUniversity of [email protected]

Fabio PasqualettiDepartment of Mechanical EngineeringUniversity of California, Riverside, [email protected]

Matthew Ceislak, Scott GraftonDepartment of Psychological and Brain SciencesUniversity of California, Santa Barbara, [email protected], [email protected]

Danielle S. BassettDepartment of Electrical & Systems Engineering,University of Pennsylvania, Philadelphia, [email protected]

PP2

Compressive Sensing with Exactly Solvable Chaos

Recent advances in sampling theory allow the reconstruc-tion of signals sampled at sub-Nyquist rates. Compres-sive sensing operates under the premise that signal acqui-sition and data compression can be carried out simultane-ously. Building on recent work in chaotic communications,a compressive negative Beta encoder/decoder is presentedthat represents data in an irrational radix. Using an exactchaotic oscillator and pulsed linear filter, a complete A/Dand D/A architecture based on chaotic dynamics can bebuilt in hardware.

Sidni Hale, Anthony DiPofi, Bradley KimbrellRadix [email protected], [email protected],[email protected]

PP2

Identifying the Role of Store-Operated CalciumChannels in Astrocytes Via An Open-Cell Model

Astrocytes are the most common glial cells in the brain,communicating via calcium transients, and possibly mod-ulating neuronal signals. However, these calcium dynamicsdiffer between in vivo and in vitro. We suggest a new open-cell mathematical model that allows us to vary parameterssuch as cell volume and flux through calcium channels noteasily accessible by experimentalists. Our results supportthe idea that store-operated calcium channels play a keyrole, and suggest realistic, follow-up experiments.

Gregory A. HandyUniversity of Utah Mathematics [email protected]

Alla BorisyukUniversity of UtahDept of [email protected]

Marsa TaheriUniversity of UtahDepartment of [email protected]

John Whitedepartment of Bioengineering

226 DS15 Abstracts

The University of [email protected]

PP2

Behavioral Dynamics and STD Transmission

Many mathematical models of infectious disease transmis-sion represent contact patterns using fixed rate parameters.However, individual contact and protective behaviors arelikely to respond elastically to disease outbreaks. We usethe replicator-mutator equations from evolutionary gametheory to couple the dynamics of protective sexual behav-ior to a simple SIS compartmental model. Our combinedmodel demonstrates a shift in effective contact reductionbehavior over the course of the outbreak, driven by thebehavioral-disease interaction dynamics.

Michael A. HayashiUniversity of Michigan School of Public [email protected]

Marisa EisenbergUniversity of [email protected]

PP2

Master Stability Functions for the Fixed Point So-lution of Synchronized Identical Systems with Lin-ear Delay-Coupling and a Single Constant Delay

This poster presents master stability functions for the fixedpoint solution of any network of synchronized identical sys-tems with linear delay-coupling and a single constant delay.The connection between these master stability functionsand amplitude death islands is also provided using numer-ical simulations of small oscillator networks with identicalchaotic node dynamics.

Stanley R. Huddy, Jie SunClarkson [email protected], [email protected]

PP2

Rigorous Numerics for Analytic Solutions of Differ-ential Equations: The Radii Polynomial Approach

The radii polynomial method has been used for validatingnumerical approximations to Ck periodic solutions of dif-ferential equations. This paper discusses the extension (viaweighted Fourier sequence spaces) of the method to solu-tions in the analytic category, which often leads to betterbounds and the possibility of continuation of the solutionas a manifold in parameter space. It then details two exam-ples in which our numerics have led us to computer-assistedproof of solutions.

Allan R. HungriaUniversity of [email protected]

Jean-Philippe LessardUniversite [email protected]

Jason Mireles-JamesDepartement of MathematicsFlorida Atlantic University

[email protected]

PP2

Windows of Opportunity: Synchronization in On-Off Stochastic Networks

We study dynamical networks whose topology and intrin-sic parameters stochastically change, on a time scale thatranges from fast to slow. When switching is fast, thestochastic network synchronizes as long as synchronizationin the averaged network, becomes stable. We prove globalstability of synchronization in the fast switching limit. Be-yond fast switching, we reveal unexpected windows of in-termediate switching frequencies in which synchronizationbecomes stable despite the instability of the averaged/fast-switching network.

Russell JeterGeorgia State [email protected]

Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected]

PP2

Two-Theta Neuron: Phase Models for BurstingNetworks

We continue our reduction approach to study bursting out-comes of central pattern generators using coupled two-theta phase models. We examine configurations of 3-cellCPGs with inhibitory, excitatory and electrical synapses,and model and compare with corresponding real-world ex-emplary networks. Occurrence, robustness and transfor-mations of CPG outcomes are studied using 2D returnmaps, stable fixed points and invariant circles correspondto bursting patterns with fixed and varying phase lags.

Aaron [email protected]

PP2

A mathematical model for adaptive crawling loco-motion

Crawling with locomotory wave is a fundamental methodof biological locomotion in invertebrate including limblessand legged animals. We conducted observations of crawlinglocomotion in largely different conditions. In particular, itwas found that centipedes can variously change their leg-density waves which represent spatio-temporal coordina-tion pattern of ground friction. Here, we present a simplemechano-mathematical model for crawler so that it pro-vides observed mode transition depending on the external/ internal conditions.

Shigeru KurodaResearch Institute for Electronic Science,Hokkaido [email protected]

Toshiyuki NakagakiRearch Institute for Electronical ScienceHokkaido University

DS15 Abstracts 227

[email protected]

PP2

Canard-Mediated Dynamics in a Phantom Burster

We present canard-mediated dynamics arising in a phan-tom burster, formed by a multiple timescale model com-posed of FitzHugh-Nagumo systems, which represents analternating pulse and surge pattern in a neuro-secretorycontext. So far, global and local features of the modelhave been studied in the context of slow-fast dynamics andmixed-mode oscillations where folded singularities and as-sociated canard trajectories have a particular importance.Here, we study the effect of the folded singularities in slow-fast transitions.

Elif Koksal Ersoz, Mathieu Desroches, Maciej Krupa,Frederique CleementINRIA [email protected], [email protected], [email protected], [email protected]

PP2

Effective Dispersion Relation of the NonlinearSchrodinger Equation

The linear part of the Nonlinear Schrodinger Equation(NLS) (iqt = qxx) has dispersion relation ω = k2. We don’tnecessarily expect solutions to the NLS to behave nicely orhave any kind of effective dispersion relation, since we ex-pect nonlinear waves to be strongly coupled and not sinu-soidal in time. However, I have seen that solutions to theNLS are actually weakly coupled and are often nearly si-nusoidal in time with a dominant frequency. In fact, whenI look at long-time average of either a solution with manysolitons or with many unstable modes, the power spec-tral density does indicate a quadratic dispersion relationthat has been shifted by a constant proportional to theamplitude of the initial condition: ω = k2 − 2A where

A = ‖q(k,0)‖22π

. I will show a number of plots confirmingthis.

Katelyn J. Leisman, Gregor KovaCiCRensselaer Polytechnic [email protected], [email protected]

David CaiNew York UniversityCourant [email protected]

PP2

Mathematical Model of Bidirectional VesicleTransport and Sporadic Capture in Axons

We model the transport of vesicles along an axon using anadvection-diffusion equation which includes vesicle degra-dation and sporadic capture by presynaptic targets. Ourmodel shows that the steady state concentration of vesiclesdistributed along the axon does not decay exponentiallyin space for some parameter values. We also study howheterogeneity in the distribution of targets can enhancecargo delivery by performing a multi-scale homogenizationin space.

Ethan LevienUniversity of [email protected],edu


PP2

Modelocking in Chaotic Advection-Reaction-Diffusion Systems

Systems undergoing chaotic advection-reaction-diffusiondynamics have rich topological structures that define thefront propagation. Here we use burning invariant manifolds(BIMs) to provide a theoretical framework that explainsmodelocking as observed experimentally and in numericalsimulations. The existence of a relative periodic orbit andthe shape of the BIM determine the type of modelock-ing. Using this technique we find higher order modelock-ing types and discuss the switching of modelocking typesobserved in experiments.

Rory A. [email protected]



PP2

Effect of Multi-Species Mass Emergence on Biodi-versity

Mass emergences are a regular occurrence in rivers andstreams. Many aquatic insects depend on safety in num-bers to escape the water and reproduce. This strategynot only allows individual species to enhance reproductivesuccess by reducing predation rates, but also creates op-portunities for scarcer species that synchronize their emer-gence with more prevalent species. We construct a heuris-tic model to study inherent protections afforded by biodi-versity and consider implications for repopulation effortsin pollution-impacted systems.

James E. McClureAdvanced Research ComputingVirginia [email protected]

Nicole AbaidVirginia Polytechnic Institute and State [email protected]

PP2

A B Cell Receptor Signaling Model and DynamicOrigins of Cell Response

The kinase Syk is imperative for the intricate signalingevents that occur in B cells, events which lead to cellularresponses when antigens bind to B cell receptors (BCRs).We have constructed a deterministic model for BCR signal-ing centered around Syk. After tuning feedbacks betweenkey kinases and phosphatases, we demonstrated qualitativeagreement between the model and dose response data from

228 DS15 Abstracts

literature. We investigate the role of positive and negativefeedbacks in determining cell response.

Reginald McgeePurdue [email protected]

PP2

Stability of Morphodynamic Equilibria in TidalBasins

Interesting bed patterns are observed in the tidal basinsof, for example, the Wadden Sea along the Dutch, Ger-man and Danish coast. To get a better understanding ofthese phenomena, a morphodynamic model has been con-structed. The goal is to find the morphodynamic equilibriaand their stability, and to investigate their sensitivity toparameter variations. Therefore, the equations have beenscaled and asymptotically analysed. Using finite elementmethod and continuation techniques, the equilibrium of thebed has been determined.

Corine J. MeermanLeiden UniversityMathematical [email protected]

Vivi RottschaferDepartment of MathematicsLeiden [email protected]

Henk SchuttelaarsDelft Institute of Applied MathematicsDelft University of [email protected]

PP2

Frequency-Dependent Left-Right Coordination inLocomotor Pattern Generation

Coordination between left and right activities in the spinalcord during locomotion is controlled by commissural in-terneurons (CINs). Several types have been geneticallyidentified including both excitatory (VOV) and inhibitory(V0D). Genetic elimination of these CINs caused switch-ing from a normal left-right alternation to a left-right syn-chronized pattern. Ablation of V0D neurons resulted ina lack of left-right alternation at low locomotor frequen-cies, whereas selective ablation of V0V CINs switched themotor output to a left-right synchronized pattern at highfrequencies. We developed a model of neural circuits con-sisting of four pacemaker neurons, left and right flexorsand extensors, interacting via V0D and V0V commissuralpathways. The model reproduced all experimentally iden-tified regimes in the corresponding frequency ranges. Wequalitatively analyzed the behavior of this network in theabove regimes and transitions between them.

Yaroslav MolkovIndiana University - Purdue University [email protected]

Bartholomew Bacak, Ilya A. RybakDrexel University College of Medicine


PP2

Capacity for Learning the Shape of Arena in theSingle-Celled Swimmer, Viewed from Slow Dynam-ics of Membrane Potential.

We have studied for some years the learning capacity fortime and space in unicellular organisms. Here we presentthat protozoan ciliates, Paramecium and Tetrahymena,show the swimming trajectory adaptive to the shape (e.g.capillary and droplet) of swimming arena in which theyexperienced just before. As the swimming activity is reg-ulated by membrane potential in the ciliates, a possiblemechanism is considered according to the equations ofHodgkin-Huxley type with the additional slower variable.

Toshiyuki NakagakiRearch Institute for Electronical ScienceHokkaido [email protected]

Itsuki KunitaHokkaido [email protected]

Tatsuya YamaguchiKyushu Universitytatsuya [email protected]

Masakazu AkiyamaHokkaido [email protected]

Atsushi TeroKyushu [email protected]

Shigeru KurodaResearch Institute for Electronic Science,Hokkaido [email protected]

Kaito OokiHokkaido [email protected]

PP2

Co-Dimension Two Bifurcations in Piecewise-Smooth Continuous Dynamical Systems

The mean-field equations for a network of type I neurons isa piecewise-smooth continuous (PWSC) system of ordinarydifferential equations. This system displays two prominentco-dimension two non-smooth bifurcations involving colli-sions of a saddle-node equilibrium with a switching man-ifold, and a Hopf equilibrium with a switching manifold.These bifurcations are analytically resolved for the mean-field system in full detail. The genericity of these bifur-cations for an arbitrary PWSC system is also discussed.

Wilten NicolaUniversity of [email protected]

Sue Ann CampbellUniversity of Waterloo

DS15 Abstracts 229

Dept of Applied [email protected]

PP2

Analysis of Malaria Transmission Dynamics withSaturated Incidence

Mathematical model for malaria transmission in a two-interacting population with saturated incidence was for-mulated and robustly analysed. The model was shown toexhibit a subcritical bifurcation whenever a unique thresh-old, R0, increases through unity. However, under specificconditions, globally asymptotically stable malaria-free andendemic equilibria were established at R0 < 1 and R0 > 1respectively. Further, sensitivity analysis and simulationswere performed to examine the effects of some parameterson the model.

Samson OlaniyiDepartment of Pure and Applied MathematicsLadoke Akintola University of Technology, [email protected]

PP2

Temporally Periodic Neural Responses from Spa-tially Periodic Stimuli

Certain static spatial visual patterns induce temporallyvarying neural responses, such as in pattern-sensitiveepilepsy and some visual illusions. These temporal re-sponses are often strong only in a very narrow spatialfrequency band and nonexistent at other spatial frequen-cies. We present a spatially distributed neural field modelthat captures this resonant behavior in simulations, anddemonstrate analytically this strong sensitivity to the spa-tial wavelength with a perturbation calculation near theinstability.

Jason E. PinaUniversity of Pittsburgh Department of [email protected]


PP2

Using a Stochastic Field Theory to UnderstandCollective Behavior of Swimming Microorganisms

Large groups of active particles can show collective behav-ior and enhanced fluctuations, but mean field theories tounderstand them ignore fluctuations. We have extendedthese field theories to include stochastic fluxes and havequantified the dynamics in terms of enhanced diffusionand mixing and number fluctuations. We have also com-pared with results with the mean field theory and discreteparticle-based simulations.

Yuzhou QianRensselaer Polytechnic [email protected]


Patrick UnderhillRensselaer Polytechnic [email protected]

PP2

Consensus and Synchronization over Biologically-Inspired Networks: From Collaboration to Antag-onism

The vast majority of work on consensus and synchroniza-tion of coupled dynamical systems considers their interac-tions to be collaborative. In our present work, we studytwo different networks representing more realistic scenar-ios; one consists of dynamic leaders in a collaborative net-work and another consists of agonistic and antagonistic in-teractions. We establish closed form results for the rate ofconvergence to consensus for both the cases and conditionsfor stochastic synchronization in the second case.

Subhradeep Roy, Nicole AbaidVirginia Polytechnic Institute and State [email protected], [email protected]

PP2

Oscillatory Shear Flow Influence on the Two PointVortex Dynamics

Bounded and unbounded quasi-periodic dynamics of twopoint vortices of unequal strengths embedded in an oscilla-tory shear flow with rotation is addressed with an emphasison their impact on passive tracer transport. All the sets ofthe vortex signs are shown to induce qualitatively divergenttransport patterns. Regions enduring effective stretching,and consequently prone to intense mixing are identified bymeans of finite-time Lyapunov exponents.

Evgeny RyzhovV.I. Ilichev Pacific Oceanological [email protected]

Konstantin KoshelV.I. Ilichev Pacific Oceanological InstituteFar Eastern Federal [email protected]

PP2

Waveaction Spectra for Fully Nonlinear MMTModel

We investigate a version of the Majda-McLaughlin-Tabakmodel of dispersive wave turbulence where the linear termin the time derivative is removed. We are interested inthe long-time average of the distribution of waveactionthroughout the system as a function of wavenumber. Weconsider driven-damped and undriven, undamped cases ofthe model. Our theoretical predictions, which include self-similarity arguments and statistical mechanical methods,are found to agree with time dynamics simulations.

Michael SchwarzRensselaer Polytechnic [email protected]


230 DS15 Abstracts



PP2

Wild Dynamics in Nonlinear Integrate-and-FireNeurons: Mixed-Mode Bursting, Spike Adding andChaos.

Nonlinear integrate-and-fire neuron models are hybrid dy-namical systems combining continuous differential equa-tions and discrete resets, where spikes are defined by thedivergence of the membrane potential to infinity. The na-ture of the spike pattern has been related to the orbits ofa discrete map, the adaptation map, which was studied ina number of situations where it was regular. We analyzehere cases of discontinuous adaptation map and show thatextremely wild behaviors can appear.

Justyna H. SignerskaINRIA MYCENAE Laboratory, Paris;Mathematical Neuroscience Lab, CIRB College de [email protected]

Jonathan D. TouboulThe Mathematical Neuroscience LaboratoryCollege de France & INRIA [email protected]

Alexandre VidalUniversity of Evry-Val-d’EssonneDepartment of Mathematics - Analysis and [email protected]

PP2

Return Times and Correlation Decay in LinkedTwist Maps

Linked twist maps form an archetypal class of non-uniformly hyperbolic system, of particular relevance tofluid mixing. Previous results demonstrate that they havea polynomial decay of correlations. Of practical interest isthe time at which the system begins to experience this alge-braic tail in the decay, after the faster, chaotic, exponentialmixing has taken place.

Rob SturmanUniversity of [email protected]

PP2

Osteocyte Network Formation

We construct a model of a dynamic network that consists ofosteocytes, a type of cell within bone. On the bone-tissueinterface, osteoblasts secrete the osteoid bone matrix andmulti-nucleated osteoclasts resorb it. These osteoblastscan also differentiate into osteocytes. In pathological bone,the highly regulated bone remodelling signalling pathwayis disrupted. By understanding these dynamics, we hope

to gain insights into how to predict structural differencesbetween healthy and cancerous tissue.

Jake P. Taylor-KingMathematical Institute, The University of [email protected]

Mason A. PorterUniversity of OxfordOxford Centre for Industrial and Applied [email protected]

Jon ChapmanMathematical InstituteThe University of [email protected]

David BasantaIntegrated Mathematical OncologyMoffitt Cancer [email protected]

PP2

On a FitzHugh-Nagumo Kinetic Model for NeuralNetworks

This paper undertakes the analysis of the existence anduniqueness of solutions for a mean-field FitzHugh-Nagumoequation arising in the modeling of the macroscopic ac-tivity of the brain. In particular, we prove existence ofsolution and non trivial stationary solution to evolutionequation without restriction on the connectivity coefficientε > 0 and, using a semigroup factorisation method in Ba-nach spaces, uniqueness of the stationary solution and itsexponential NL stability in the small connectivity regime.

Cristobal QuininaoLaboratoire Jacques-Louis [email protected]

Jonathan D. TouboulThe Mathematical Neuroscience LaboratoryCollege de France & INRIA [email protected]

Stephane MischlerUniversite [email protected]

PP2

Examining Partial Cascades in Clustered Networkswith High Intervertex Path Lengths

There has been significant study of cascades on networkswith various properties. There is a well-known branchingprocess approach developed by James Gleeson that is usefulfor sparse locally treelike networks, particularly those withlow mean intervertex path lengths. We examine methodsto apply to networks with longer intervertex path lengths,which may contribute to a partial cascade not seen withGleeson’s method.

Yosef M. TreitmanRensselaer Polytechnic [email protected]

Peter R. KramerRensselaer Polytechnic Institute

DS15 Abstracts 231

Department of Mathematical [email protected]

PP2

Almost Complete Separation of a Fluid Compo-nent from a Mixture Using the Burgers Networksof Micro-separators

Two ways of networking micro-separators to separate hy-drogen, for example, from a mixture almost completelyare proposed. Each separator has two outlets for slightlyhigher and lower concentrations whose difference is mod-eled by a quadratic map of the average concentration atits inlet. In the continuum the networks are governed bythe Burgers equation or its variant with nonlinear no-fluxboundary conditions. The initial boundary value problemis exactly solvable. A family of equilibria attract globally.The target component is shown to be extracted from oneside of a stationary shock. Micro-devices for testing theidea are also proposed.

Shinya WatanabeMathematics & InformaticsIbaraki [email protected]

Sohei MatsumotoResearch Center for Ubiquitous MEMS and MicroEngineering,National Inst. of Advanced Industrial Science &[email protected]

Tomohiro Higurashi, Yuya Yoshikawa, Naoki OnoDepartment of Engineering Science and MechanicsShibaura Institute of [email protected], [email protected],[email protected]

PP2

New Data Anysis Approach for Complex Signalswith Low Signal to Noise Ratio’s

We propose a toolbox for signals comparisons with lowSNR. We combine techniques from dynamical systems andinformation theory to quantify and extract information inthe data sets. Data sets with SNR’s of 0.3 to 0.002 were an-alyzed. Useful information was found and quantized withtight bounds on the estimate. We also compare to Gaus-sian noise and show our toolbox can be used to separatesignals with low SNR from white noise.

Jeremy WojcikGeorgia State UniversityDept. Mathematics and [email protected]

PP2

Data Assimilation for Traffic State and ParameterEstimation

Our goal is to apply data assimilation techniques to mi-croscopic and macroscopic traffic models to estimate traf-fic states and parameters. We found ways in which sensordata as well as GPS data of moving cars can be assimilatedin a unified freeway. We implemented this approach usingboth ensemble Kalman and particle filter and evaluatedtheir efficacy using microscopic and macroscopic models.

We applied our results to real traffic data from MinnesotaTransportation Department.

Chao XiaBrown Universitychao [email protected]

Bjorn Sandstede, Paul CarterDivision of Applied MathematicsBrown Universitybjorn [email protected], paul [email protected]


PP2

Stochastic Active-Transport Model of Cell Polar-ization

We present a stochastic model of active vesicular trans-port and its role in cell polarization, which takes intoaccount positive feedback between membrane-bound sig-naling molecules and cytoskeletal filaments. In particular,we consider the cytoplasmic transport of vesicles on a two-dimensional cytoskeletal network, in which a vesicle con-taining signaling molecules can randomly switch betweena diffusing state and a state of directed motion along afilament. We show that the geometry of the cytoskeletalfilaments plays a crucial role in determining whether thecell is capable of spontaneous cell polarization or only po-larizes in response to an external chemical gradient.Theformer occurs if filaments are nucleated at sites on the cellmembrane (cortical actin), whereas the latter applies if thefilaments nucleate from organizing sites within the cyto-plasm (microtubule asters).

Bin XuUniversity of Utah, salt lake city,[email protected]


PP2

Statistical Properties of Finite Systems of Point-Particles Interacting Through Binary Collisions

In a finite system of point-particles interacting through bi-nary collisions, particles number of collisions and time oflast collision are functions of the initial distributions ofthe positions and velocities of all particles. We investi-gate a one-dimensional system of N particles interactingthrough either elastic or inelastic collisions. In particular,given random initial particle positions and velocities, weestablish formulae for the distributions of the number ofcollisions and final collision times.

Alexander L. YoungUniversity of ArizonaProgram in Applied [email protected]

Joceline LegaUniversity of Arizona, [email protected]

232 DS15 Abstracts

Sunder SethuramanUniversity of ArizonaDepartment of [email protected]

PP2

Heteroclinic Separators of Magnetic Fields in Elec-trically Conducting Fluids

We partly solve the problem of existence of separators of amagnetic field in plasma. We single out in plasma a 3-bodywith a boundary in which the movement of plasma is ofspecial kind which we call an (a-d)-motion. The statementof the problem and the suggested method for its solutionlead to some theoretical problems from Dynamical SystemsTheory. The work was supported by RFBR, Grants 12-01-00672-a and 13-01-12452-ofi-m.

Evgeny ZhuzhomaNational Research University Higher School of [email protected]

Vyatcheslav Grines, Timur MedvedevLobachevsky State University of Nizhni [email protected], [email protected]

Olga PochinkaNational Research University Higher School of [email protected]


Or ganizer and Speaker Index

2015


Berger, Mitchell, MS92, 1:30 Wed

Bergman, Lawrence, MS45, 9:00 Tue

Bernoff, Andrew J., MS71, 4:00 Tue

Bertozzi, Andrea L., IP2, 11:00 Mon

Bhattacharyya, Samit, CP8, 4:30 Sun

Bialonski, Stephan, PP2, 8:30 Wed

Bianco, Simone, MS67, 1:30 Tue

Bianco, Simone, MS67, 1:30 Tue

Bick, Christian, MS27, 9:30 Mon

Biktashev, Vadim N., MS80, 8:30 Wed



Biktasheva, Irina, MS65, 1:30 Tue



Billings, Lora, PD1, 7:00 Mon

Birnir, Bjorn, MS11, 9:30 Sun

Bittihn, Philip, MS64, 2:00 Tue

Blackmore, Denis, MS39, 1:15 Mon

Blackmore, Denis, MS39, 1:15 Mon

Blackmore, Denis, MS52, 8:30 Tue

Bloch, Anthony M., MS22, 8:30 Mon

Blömker, Dirk, MS120, 8:30 Thu

Boatto, Stefanella, MS79, 8:30 Wed



Boccaletti, Stefano, MS68, 1:30 Tue

Bodenschatz, Eberhard, MS65, 2:00 Tue

Boechler, Nicholas, MS83, 9:00 Wed

Bogacz, Rafal, MS114, 9:30 Thu

Boie, Sebastian D., PP1, 8:30 Tue

Bollt, Erik, MS44, 1:45 Mon

Bondarenko, Vladimir E., CP21, 4:25 Mon

Bonet, Carles, CP9, 4:50 Sun

Bose, Amitabha, MS25, 8:30 Mon

Bose, Amitabha, MS25, 8:30 Mon

Bose, Chris, MS44, 1:15 Mon

Bose, Chris, MS44, 1:15 Mon

Bossolini, Elena, PP2, 8:30 Wed

Bounkhel, Messaoud, MS91, 3:00 Wed

Braatz, Richard D., MS82, 8:30 Wed

BBagrow, James, MS102, 1:30 Wed

Bai, Lu, MS120, 9:00 Thu

Bakker, Berry, CP1, 5:50 Sun

Balasuriya, Sanjeeva, MS111, 8:30 Thu



Bamieh, Bassam A., MS124, 2:00 Thu

Banerjee, Soumitro, MS49, 9:30 Tue

Bansal, Shweta, MS85, 9:00 Wed

Barbaro, Alethea, MS11, 9:00 Sun

Barbaro, Alethea, MS11, 9:00 Sun

Barbaro, Alethea, MS29, 8:30 Mon

Barkley, Dwight, MS80, 9:00 Wed

Barranca, Victor, MS7, 9:00 Sun

Barranca, Victor, MS7, 9:00 Sun

Barreiro, Andrea K., MS51, 8:30 Tue

Barreiro, Andrea K., MS51, 8:30 Tue

Barreto, Ernest, MS117, 8:30 Thu

Barreto, Ernest, MS129, 1:30 Thu

Barrio, Roberto, MS119, 3:00 Wed

Barry, Anna M., MS100, 2:00 Wed

Bartoloni, Bruno, PP2, 8:30 Wed

Barton, David A., CP6, 5:10 Sun

Basarab, Casayndra H., PP1, 8:30 Tue

Basnarkov, Lasko, MS41, 2:45 Mon

Basnayake, Ranil, PP2, 8:30 Wed

Bassett, Danielle, MS89, 9:30 Wed

Bates, Peter W., MS70, 2:30 Tue

Bauver, Martha, PP1, 8:30 Tue

Beal, Aubrey N., MS43, 2:15 Mon

Beaume, Cedric, CP14, 3:45 Mon

Bellman, Jacob, PP2, 8:30 Wed

Bellsky, Thomas, MS63, 2:00 Tue

Belykh, Igor, MS12, 9:00 Sun

Belykh, Igor, MS12, 9:00 Sun

Belykh, Igor, MS30, 8:30 Mon

Benichou, Olivier, MS81, 10:00 Wed

Ben-Naim, Eli, PD1, 7:00 Mon

Berdeni, Yani, MS133, 2:30 Thu

Berg, Sebastian, MS15, 3:00 Sun

AAbaid, Nicole, MS12, 10:00 Sun

Abarbanel, Henry D., MS61, 1:30 Tue

Abarbanel, Henry D., MS101, 1:30 Wed

Abel, Markus, MS53, 10:00 Tue

Abramov, Rafail, MS69, 1:30 Tue

Abramov, Rafail, MS69, 1:30 Tue

Abrams, Daniel, MS12, 9:30 Sun

Abud, Celso, PP1, 8:30 Tue

Acosta-Humanez, Primitivo B., CP19, 4:45 Mon

Adams, Ronald, CP10, 5:30 Sun

Aguilar, Luis T., MS23, 9:30 Sun

Aguirre, Pablo, MS57, 8:30 Tue

Aguirre, Pablo, MS108, 4:00 Wed

Ahmad, Mohd Ashraf, MS54, 9:00 Tue

Ahn, Sungwoo, PP2, 8:30 Wed

Akao, Akihiko, PP1, 8:30 Tue

Alacam, Deniz, PP2, 8:30 Wed

Albers, David J., MS6, 1:30 Thu

Albers, David J., MS6, 2:30 Thu

Albers, John R., MS48, 8:30 Tue

Alexeev, Timur, CP7, 4:30 Sun

Al-Hdaibat, Bashir M., CP19, 3:45 Mon

Alipova, Bakhyt, CP10, 4:30 Sun

Alolyan, Ibraheem, PP1, 8:30 Tue

Altaner, Bernhard, MS75, 4:00 Tue

Altaner, Bernhard, MS75, 4:00 Tue

Amann, Andreas, CP11, 5:10 Sun

Amann, Andreas, MS106, 4:00 Wed

Ameli, Siavash, PP2, 8:30 Wed

Ansmann, Gerrit, MS31, 9:00 Mon

Aoi, Shinya, MS112, 8:30 Thu

Aoki, Takaaki, CP3, 5:10 Sun

Arbabi, Hassan, MS42, 1:45 Mon

Argyris, Apostolos, PP2, 8:30 Wed

Arioli, Gianni, CP7, 5:50 Sun

Arloff, William D., PP1, 8:30 Tue

Arroyo-Almanza, Diana A., CP23, 5:25 Mon

Assaf, Michael, MS46, 8:30 Tue

Assaf, Michael, MS46, 8:30 Tue

Avedisov, Sergei S., CP3, 4:30 Sun

Italicized names indicate session organizers.


DDalena, Serena, PD1, 7:00 Mon

Dankowicz, Harry, MS100, 3:00 Wed

Das, Sanjukta, CP11, 5:30 Sun

Dawes, Jonathan, PP2, 8:30 Wed

Dawson, Scott, MS55, 9:00 Tue

Day, Sarah, MS128, 2:30 Thu

de Barros Viglioni, Humberto H., MS79, 10:00 Wed

De Maesschalck, Peter, MS118, 9:00 Thu

De Rijk, Björn, MS70, 3:00 Tue

De Sousa, Meirielen C., PP1, 8:30 Tue

del Genio, Charo I., MS68, 1:30 Tue

del Genio, Charo I., MS68, 2:30 Tue

Della Rossa, Fabio, CP18, 4:25 Mon

Dellnitz, Michael, MS103, 2:30 Wed

Denner, Andreas, MS103, 3:00 Wed

DeSantis, Mark, CP26, 4:00 Tue

Desbrun, Mathieu, MS79, 8:30 Wed

Desroches, Mathieu, MS118, 8:30 Thu



D’Huys, Otti, MS2, 10:30 Sun

Dias, Juliana, MS48, 8:30 Tue

Dias, Juliana, MS48, 9:30 Tue

Dierckx, Hans, MS80, 9:30 Wed

Ding, Xiong, CP10, 5:50 Sun

Dobreva, Atanaska, MS90, 9:30 Wed

Doelman, Arjen, MS19, 10:00 Mon

Doelman, Arjen, MS123, 1:30 Thu

Doering, Charles, PD1, 7:00 Mon

Donohue, John G., CP5, 5:30 Sun

Dorfler, Florian, MS107, 4:00 Wed

Dorfler, Florian, MS107, 4:30 Wed

D’Orsogna, Maria, MS81, 8:30 Wed

Dostal, Leo, CP10, 5:10 Sun

Drotos, Gabor, MS58, 3:00 Tue

Duan, Jinqiao, MS120, 8:30 Thu



Duncan, Jacob P., CP5, 4:50 Sun

Chan, Matthew H., PP1, 8:30 Tue

Chandrashekar, Pooja, PP2, 8:30 Wed

Charalampidis, Efstathios, CP23, 4:05 Mon

Chen, Diandian Diana, MS28, 8:30 Mon

Chen, Qianting, PP1, 8:30 Tue

Chen, Xiaopeng, MS120, 8:30 Thu



Cherry, Elizabeth M., MS15, 2:00 Sun

Cherry, Elizabeth M., MS65, 2:30 Tue

Cheviakov, Alexei F., MS81, 9:00 Wed

Chong, Antonio S., PP1, 8:30 Tue

Chong, Christopher, MS45, 9:30 Tue

Christov, Ivan C., MS39, 2:45 Mon

Chuang, Yaoli, MS88, 9:30 Wed

Ciocanel, Veronica M., PP2, 8:30 Wed

Clifton, Sara, CP5, 4:30 Sun

Cogan, Nick, MS90, 8:30 Wed

Cohen, Seth D., MS43, 1:45 Mon

Collens, Jarod, MS50, 9:00 Tue

Colombo, Giovanni, MS78, 9:30 Wed

Colonius, Fritz, CP19, 4:05 Mon

Comtois, Philippe, MS65, 3:00 Tue

Consagra, William, PP2, 8:30 Wed

Contreras, Christy, PP1, 8:30 Tue

Conway, Jessica M., MS85, 8:30 Wed



Corron, Ned J., MS43, 1:15 Mon

Corron, Ned J., MS43, 1:15 Mon

Cousins, Will, MS110, 9:30 Thu

Creaser, Jennifer L., MS57, 9:30 Tue

Criado, Regino, MS68, 1:30 Tue

Criado, Regino, MS68, 1:30 Tue

Cumings, Karen M., PP2, 8:30 Wed

Cummings, Linda, MS124, 3:00 Thu

Cummins, Bree, PP1, 8:30 Tue

Curran, Mark J., CP1, 4:50 Sun

Czechowski, Aleksander, CP1, 5:30 Sun

Bradley, Elizabeth, CP22, 4:25 Mon

Brena-Medina, Victor F., CP29, 4:40 Tue

Bressloff, Paul C., MS105, 4:00 Wed

Bröcker, Jochen, MS61, 1:30 Tue

Bröcker, Jochen, MS61, 1:30 Tue

Brons, Morten, MS52, 10:00 Tue

Brooks, Heather A., PP2, 8:30 Wed

Brubaker, Douglas, MS29, 8:30 Mon

Brunel, Nicolas, MS74, 4:30 Tue

Brunton, Bing W., MS42, 2:45 Mon

Brunton, Steven, MS42, 1:15 Mon

Brunton, Steven, MS55, 8:30 Tue

Brunton, Steven, MS55, 10:00 Tue

Budanur, Nazmi Burak, CP19, 4:25 Mon

Budd, Chris, MS36, 1:15 Mon

Budisic, Marko, MS92, 3:00 Wed

Budisic, Marko, MS111, 8:30 Thu

Budisic, Marko, MS124, 1:30 Thu

Burke, Korana, CP15, 5:25 Mon

Burke, Korana, MS62, 1:30 Tue

Burli, Pralhad, PP1, 8:30 Tue

Butlin, Tore, MS133, 3:00 Thu

Byrne, Greg A., MS28, 9:00 Mon

CCafaro, Carlo, CP18, 5:25 Mon

Caiola, Michael, PP1, 8:30 Tue

Caldas, Iberê L., MS24, 10:00 Mon

Calderer, Maria-Carme, MS97, 4:00 Tue

Camp, Charles D., CP12, 5:30 Sun

Campbell, David, PD1, 7:00 Mon

Campbell, Sue Ann, CP22, 3:45 Mon

Canadell, Marta, PP2, 8:30 Wed

Candelier, Fabien, MS35, 2:15 Mon

Carja, Oana, MS67, 3:00 Tue

Carr, Thomas W., PP2, 8:30 Wed

Carroll, Samuel R., MS66, 3:00 Tue

Carroll, Thomas L., MS101, 1:30 Wed

Carroll, Thomas L., MS101, 3:00 Wed

Carter, Paul A., MS40, 1:15 Mon

Carter, Paul A., MS70, 2:00 Tue

Champneys, Alan R., MS112, 8:30 Thu



Giusti, Chad, MS14, 2:00 Sun

Glasner, Karl, MS1, 9:30 Sun

Glass, Leon, MS2, 10:00 Sun

Glendinning, Paul, MS87, 9:00 Wed

Gluckman, Bruce J., MS6, 3:00 Thu

Godec, Aljaz, MS81, 9:30 Wed

Goel, Pranay, MS109, 5:30 Wed

Gog, Julia R., MS85, 10:00 Wed

Goh, Ryan, PP1, 8:30 Tue

Golubitsky, Martin, MS20, 10:00 Mon

Gomez, Marcella, MS17, 3:30 Sun

Gong, Xue, PP2, 8:30 Wed

Gonzalez, Marta, MS16, 2:30 Sun

Gonzalez Tokman, Cecilia, MS44, 2:15 Mon

Gore, Jeff, IP5, 11:00 Wed

Gorur-Shandilya, Srinivas, MS115, 9:30 Thu

Gowda, Karna V., PP1, 8:30 Tue

Gowen, Savannah, MS86, 9:30 Wed

Granados, Albert, MS116, 10:00 Sun

Green, Kevin R., PP2, 8:30 Wed

Grigoriev, Roman, MS80, 8:30 Wed

Grigoriev, Roman, MS93, 1:30 Wed

Grinberg, Itay, MS96, 2:00 Wed

Grooms, Ian, MS8, 9:00 Sun

Groothedde, Chris M., PP1, 8:30 Tue

Grover, Piyush, CP4, 6:10 Sun

Grudzien, Colin J., CP10, 4:50 Sun

Gu, Shi, PP2, 8:30 Wed

Guckenheimer, John, SP1, 8:15 Sun

Gudoshnikov, Ivan, MS91, 2:30 Wed

Guo, Yixin, MS84, 9:30 Wed

Guo, Yixin, MS114, 8:30 Thu

Gurevich, Pavel, MS23, 10:00 Sun

Guseva, Ksenia, MS35, 2:45 Mon

HHaas, Jesse, PP1, 8:30 Tue

Hackbarth, Axel, MS21, 9:30 Mon

Hafkenscheid, Patrick, MS56, 10:00 Tue

Hagerstrom, Aaron M., CP22, 4:45 Mon

Hale, Sidni, PP2, 8:30 Wed

Haley, James M., CP26, 4:20 Tue

Hallatschek, Oskar, MS67, 2:30 Tue

Hamilton, Franz, MS15, 2:30 Sun

Folias, Stefanos, MS74, 4:00 Tue

Follmann, Rosangela, MS59, 1:30 Tue

Forgoston, Eric, MS3, 9:00 Sun

Forgoston, Eric, MS21, 8:30 Mon

Forgoston, Eric, MT2, 4:00 Wed

Forgoston, Eric, MT2, 4:00 Wed

Fox, Adam M., MS24, 9:30 Mon

Fraden, Seth, MS76, 4:30 Tue

Franci, Alessio, MS130, 2:00 Thu

Francoise, Jean-Pierre, MS118, 8:30 Thu

Freestone, Dean R., CP18, 5:05 Mon

Frey, Hans-Peter, MS6, 2:00 Thu

Froyland, Gary, MS103, 1:30 Wed

Froyland, Gary, MS103, 1:30 Wed

Fuller, Pamela B., MS51, 8:30 Tue

Fuller, Pamela B., MS51, 9:00 Tue

Funato, Tetsuro, MS112, 9:30 Thu

GGajamannage, Kelum D., CP19, 5:05 Mon

Galanthay, Theodore E., CP11, 5:50 Sun

Galuzio, Paulo, CP23, 3:45 Mon

Gandhi, Punit R., CP13, 4:30 Sun

Garg, Piyush, PP2, 8:30 Wed

Garland, Joshua, CP4, 5:10 Sun

Gauthier, Daniel J., MS31, 10:00 Mon

Gedeon, Tomas, MS2, 9:00 Sun

Gedeon, Tomas, MS2, 9:00 Sun

Gelfreich, Vassili, MS119, 1:30 Wed

Gendelman, Oleg, MS32, 1:15 Mon

Gendelman, Oleg, MS32, 1:15 Mon

Gendelman, Oleg, MS45, 8:30 Tue

Geng, Jiansheng, CP23, 4:25 Mon

Georgescu, Michael, MS41, 1:45 Mon

Ghazaryan, Anna, MS122, 8:30 Thu



Ghil, Michael, MS58, 1:30 Tue

Ghil, Michael, MS58, 1:30 Tue

Ghosh, Suma, CP5, 5:10 Sun

Ghrist, Robert W., MS14, 2:00 Sun

Girvan, Michelle, MT1, 2:00 Sun

Giusti, Chad, MS14, 2:00 Sun

Dunworth, Jeff, PP2, 8:30 Wed

Durazo, Juan, MS63, 2:30 Tue

Düren, Philipp, PP1, 8:30 Tue

Duriez, Thomas, MS111, 9:30 Thu

Dyachenko, Sergey, CP24, 4:05 Mon

Dzakpasu, Rhonda, MS84, 10:00 Wed

EEbadi, Sepideh, PP2, 8:30 Wed

Ecke, Robert E., CP14, 4:25 Mon

Edelman, Mark, CP11, 4:50 Sun

Eden, Uri, MS114, 10:00 Thu

Edwards, Roderick, MS2, 9:00 Sun

Edwards, Roderick, MS2, 9:30 Sun

Eisenberg, Marisa, CP8, 5:50 Sun

Ekrut, David A., CP2, 4:30 Sun

Emenheiser, Jeff, MS62, 2:00 Tue

Enden, Giora, MS97, 4:30 Tue

Erickson, Brittany, MS11, 9:00 Sun

Erickson, Brittany, MS11, 10:30 Sun

Erickson, Brittany, MS29, 8:30 Mon

Ermentrout, Bard, IP4, 11:00 Tue

Ermentrout, Bard, MS66, 1:30 Tue

Ermentrout, Bard, MS74, 4:00 Tue

Eubank, Stephen, MS89, 9:00 Wed

FFahroo, Fariba, PD2, 12:00 Tue

Fairchild, Michael, MS4, 10:00 Sun

Farazmand, Mohammad, CP19, 5:25 Mon

Farjami, Saeed, PP1, 8:30 Tue

Fatkullin, Ibrahim, CP24, 5:05 Mon

Fatkullin, Ibrahim, MS69, 1:30 Tue

Fenton, Flavio, MS126, 1:30 Thu

Fernandez, Oscar, MS4, 10:30 Sun

Fernandez-Garcia, Soledad, MS118, 9:30 Thu

Fessel, Kimberly, CP8, 6:10 Sun

Feudel, Ulrike, MS31, 8:30 Mon

Feudel, Ulrike, MS31, 8:30 Mon

Filo, Maurice G., CP8, 4:50 Sun

Fitzpatrick, Ben G., CP3, 5:30 Sun

Flaßkamp, Kathrin, CP11, 6:10 Sun



KKang, Wei, MS37, 1:15 Mon

Kao, Hsien-Ching, CP13, 4:50 Sun

Kapitaniak, Tomasz, CP13, 5:10 Sun

Kapitanov, Georgi, MS34, 1:45 Mon

Kapitula, Todd, MS19, 9:30 Mon

Karamchandani, Avinash J., CP13, 5:50 Sun

Karamched, Bhargav R., PP1, 8:30 Tue

Karim, Md. Shahriar, CP2, 5:30 Sun

Karrasch, Daniel, MS104, 5:30 Wed

Kasti, Dinesh, CP4, 4:50 Sun

Kath, William, MS33, 2:45 Mon

Keane, Andrew, MS106, 5:30 Wed

Kelley, Aaron, PP2, 8:30 Wed

Kelley, Douglas H., MS99, 2:00 Wed

Kelly, Scott D., MS4, 9:00 Sun

Kelly, Scott D., MS52, 8:30 Tue

Kempton, Louis, MS30, 9:30 Mon

Kenett, Dror Y., MS89, 10:00 Wed

Kepley, Shane D., CP10, 6:10 Sun

Kevrekidis, I. G., MS110, 10:00 Thu

Kevrekidis, Panayotis, MS1, 10:00 Sun

Khan, Muhammad D., CP29, 4:00 Tue

Khanin, Kostantin, MS92, 2:00 Wed

Khasin, Michael, MT2, 4:00 Wed

Kieu, Thinh T., CP4, 4:30 Sun

Kile, Jennifer, MS51, 9:30 Tue

Kiliç, Deniz K., PP1, 8:30 Tue

Kilpatrick, Zachary, MS27, 9:00 Mon

Kilpatrick, Zachary, MS66, 1:30 Tue

Kilpatrick, Zachary, MS74, 4:00 Tue

Kim, Peter S., MS34, 1:15 Mon

Kirk, Vivien, MS118, 8:30 Thu



Kirst, Christoph, MS127, 2:00 Thu

Kiss, Istvan Z., MS76, 4:00 Tue

Knapper, Drake, PP1, 8:30 Tue

Knobloch, Edgar, PD1, 7:00 Mon

Kogan, Oleg B., CP29, 5:00 Tue

Hripcsak, George, MS6, 1:30 Thu

Hsieh, Ani, MS3, 9:00 Sun

Hsieh, Ani, MS3, 9:00 Sun

Hsieh, Ani, MS21, 8:30 Mon

Hu, David, MS71, 4:30 Tue

Huddy, Stanley R., PP2, 8:30 Wed

Humpherys, Jeffrey, MS134, 1:30 Thu

Hungria, Allan R., PP2, 8:30 Wed

Hupkes, Hermen Jan, MS70, 1:30 Tue



IIams, Sarah, MS123, 3:00 Thu

Ide, Kayo, MS37, 1:45 Mon

Illing, Lucas, MS43, 1:15 Mon

Illing, Lucas, MS43, 2:45 Mon

Imura, Jun-ichi, MS41, 1:15 Mon

Imura, Jun-ichi, MS41, 2:15 Mon

Imura, Jun-ichi, MS54, 8:30 Tue

Ippei, Obayashi, MS112, 9:00 Thu

Iron, David, MS38, 1:45 Mon

JJacobs, Henry O., MS131, 1:30 Thu

Jacobs, Henry O., MS131, 2:30 Thu

Jacobsen, Karly, CP3, 5:50 Sun

James, Guillaume, MS83, 9:30 Wed

James, Ryan G., MS75, 5:00 Tue

Jaramillo, Gabriela, PP1, 8:30 Tue

Jarrett, Angela M., MS90, 8:30 Wed

Jeffrey, Mike R., MS100, 1:30 Wed

Jeter, Russell, PP2, 8:30 Wed

Ji, Yanyan, MS126, 2:30 Thu

Jiang, Jifa, MS120, 10:00 Thu

Jiang, Yazhen, CP4, 5:50 Sun

Jones, Barbara, MS67, 2:00 Tue

Jones, Kimberley, MS99, 1:30 Wed

Joshi, Badal, MS25, 9:30 Mon

Just, Winfried, CP8, 5:10 Sun

Hamzi, Boumediene, CP15, 3:45 Mon

Han, Jung Min, PP1, 8:30 Tue

Handy, Gregory A., PP2, 8:30 Wed

Haragus, Mariana, MS122, 8:30 Thu

Harker, Shaun, MS56, 9:00 Tue

Harley, Kristen, MS77, 5:00 Tue

Harris, Jeremy D., MS87, 9:30 Wed

Harris, Kameron D., MS5, 9:30 Mon

Hartmann, Carsten, MS82, 9:00 Wed

Hasan, Ragheb, PP1, 8:30 Tue

Hauert, Christoph, MS88, 10:00 Wed

Hauser, Marcus, MS73, 4:00 Tue

Hawkins, Russell, MS62, 1:30 Tue

Hayashi, Michael A., PP2, 8:30 Wed

He, YanYan, MS90, 10:00 Wed

Heckman, Christoffer R., MS3, 10:30 Sun

Heckman, Christoffer R., MS33, 1:15 Mon

Heffernan, Jane, MS85, 8:30 Wed

Hernandez-Duenas, Gerardo, MS8, 10:00 Sun

Herschlag, Gregory J., MS13, 10:30 Sun

Hess, Kathryn, MS14, 2:30 Sun

Higuera, Maria, CP14, 4:05 Mon

Hill, Kaitlin, MS36, 2:15 Mon

Hines, Paul, MS107, 5:00 Wed

Hirata, Yoshito, MS41, 1:15 Mon

Hirata, Yoshito, MS41, 1:15 Mon

Hirata, Yoshito, MS54, 8:30 Tue

Hittmeyer, Stefanie, MS108, 4:00 Wed

Hittmeyer, Stefanie, MS108, 4:00 Wed

Hjorth, Poul G., CP18, 4:05 Mon

Hoffman, Matthew J., MS15, 2:00 Sun

Hogan, John, CP9, 5:30 Sun

Holmes, Philip, MS112, 8:30 Thu

Holzer, Matt, MS134, 2:00 Thu

Homer, Martin, CP9, 5:10 Sun

Horan, Joseph, MS44, 2:45 Mon

Horesh, Raya, CP28, 4:40 Tue

Hoshino, Hikaru, PP1, 8:30 Tue

Hoyer-Leitzel, Alanna, MS36, 2:45 Mon



Ma, Yiping, MS113, 9:00 Thu

Macau, Elbert E., MS59, 1:30 Tue



Macdonald, John, MS112, 10:00 Thu

Madruga, Santiago, CP6, 4:30 Sun

Mahoney, John R., MS86, 8:30 Wed



Makarenkov, Oleg, MS78, 8:30 Wed



Makrides, Elizabeth J., MS19, 9:00 Mon

Malik, Nishant, MS89, 8:30 Wed



Mallela, Abhishek, CP28, 4:20 Tue

Malomed, Boris, MS96, 3:00 Wed

Mandal, Dibyendu, MS75, 4:30 Tue

Manevich, Leonid, MS96, 1:30 Wed

Mangan, Niall M., MS38, 1:15 Mon

Mangan, Niall M., MS38, 1:15 Mon

Manukian, Vahagn, MS122, 8:30 Thu



Marcotte, Christopher, MS80, 10:00 Wed

Martens, Erik A., MS117, 9:00 Thu

Martins, Caroline G. L., MS24, 9:00 Mon

Masoller, Cristina, MS33, 2:15 Mon

Mason, Gemma, MS4, 9:30 Sun

Matheny, Matt, MS62, 2:30 Tue

Mauro, Ava, MS94, 2:30 Wed

Mauroy, Alexandre, MS47, 10:00 Tue

Mazzoleni, Michael J., CP21, 3:45 Mon

Mcavity, David, CP21, 4:05 Mon

Mccalla, Scott, MS88, 8:30 Wed

Mccalla, Scott, MS88, 8:30 Wed

McClure, James E., PP2, 8:30 Wed

McCullen, Nick, PP1, 8:30 Tue

Mcdougall, Damon, MS21, 8:30 Mon

Mcgee, Reginald, PP2, 8:30 Wed

Lecoanet, Daniel, MS8, 9:00 Sun

Lee, Rachel, MS71, 5:00 Tue

Lee, Seungjoon, MS110, 9:00 Thu

Lega, Joceline, PD1, 7:00 Mon

Lehnert, Judith, MS106, 5:00 Wed

Lehnertz, Klaus, MS31, 8:30 Mon

Lehnertz, Klaus, MS115, 8:30 Thu

Leifeld, Julie, MS49, 9:00 Tue

Leisman, Katelyn J., PP2, 8:30 Wed

Leite da Silva Dias, Pedro, MS48, 10:00 Tue

Leok, Melvin, MS22, 9:30 Mon

Lermusiaux, Pierre, MS21, 10:00 Mon

Lessard, Jean-Philippe, MS56, 8:30 Tue

Levanova, Tatiana A., PP1, 8:30 Tue

Levien, Ethan, PP2, 8:30 Wed

Levnajic, Zoran, MS127, 2:30 Thu

Lewis, Tim, MS25, 10:00 Mon

Li, Songting, MS7, 9:30 Sun

Li, Yao, CP29, 4:20 Tue

Lilienkamp, Thomas, CP1, 5:10 Sun

Lin, Kevin K., CP15, 4:25 Mon

Lin, Lucas, PP1, 8:30 Tue

Lindenberg, Katja, MS105, 4:30 Wed

Lindsay, Alan E., MS81, 8:30 Wed



Lipson, Hod, IP7, 4:15 Thu

Liu, Di, MS69, 2:30 Tue

Lizarraga, Ian M., MS108, 5:00 Wed

Lloyd, Alun, MS85, 9:30 Wed

Locke, Rory A., PP2, 8:30 Wed

Loire, Sophie, MS111, 9:00 Thu

Lolla, Tapovan, MS37, 2:45 Mon

Lombardi, Éric, MS119, 2:00 Wed

Lopes, Sergio R., MS72, 5:00 Tue

Lopez, Vanessa, CP23, 4:45 Mon

Lundell, Fredrik, MS35, 1:45 Mon

Lushnikov, Pavel M., CP24, 4:45 Mon

MMa, Baoling, CP21, 5:05 Mon

Ma, Tian, PP1, 8:30 Tue

Köksal Ersöz, Elif, PP2, 8:30 Wed

Kolokolnikov, Theodore, MS40, 1:45 Mon

Kolokolnikov, Theodore, MS105, 4:00 Wed

Koltai, Peter, MS103, 2:00 Wed

Komarov, Maxim, MS117, 9:30 Thu

Komatsuzaki, Tamiki, MS95, 2:00 Wed

Koon, Wang-Sang, MS95, 1:30 Wed

Korda, Milan, MS131, 1:30 Thu

Korniss, Gyorgy, MS16, 2:00 Sun

Korniss, Gyorgy, MS16, 2:00 Sun

Korotkevich, Alexander O., CP24, 4:25 Mon

Kosiuk, Ilona, CP5, 5:50 Sun

Kovacic, Gregor, MS69, 2:00 Tue

Kraitzman, Noa, MS1, 9:00 Sun

Kraitzman, Noa, MS1, 9:00 Sun

Kraitzman, Noa, MS19, 8:30 Mon

Kramer, Peter R., MS29, 9:00 Mon

Kramer, Sean, CP4, 5:30 Sun

Krauskopf, Bernd, MS119, 2:30 Wed

Kristiansen, Kristian Uldall, CP9, 4:30 Sun

Krumscheid, Sebastian, MS95, 3:00 Wed

Kuehn, Christian, MS13, 9:30 Sun

Kulp, Christopher W., PP1, 8:30 Tue

Kurebayashi, Wataru, CP17, 4:25 Mon

Kuroda, Shigeru, PP2, 8:30 Wed

Kurths, Juergen, MS41, 1:15 Mon

Kurths, Juergen, MS54, 8:30 Tue

Kurths, Juergen, MS54, 8:30 Tue

Kuske, Rachel, MS17, 2:30 Sun

Kutz, J. Nathan, MS60, 2:30 Tue

LLafortune, Stéphane, MS134, 2:30 Thu

Lagor, Frank D., MS37, 2:15 Mon

Laing, Carlo R., MS129, 1:30 Thu

Lajoie, Guillaume, MS75, 4:00 Tue

Lajoie, Guillaume, MS75, 5:30 Tue

Larremore, Daniel B., MS5, 9:00 Mon

Layton, Jessica, CP12, 5:10 Sun

Lazaro, J. Tomas, MS119, 1:30 Wed

Leach, Andrew, PP1, 8:30 Tue



Ouellette, Nicholas T., MS124, 2:30 Thu

Ovsyannikov, Ivan, MS57, 8:30 Tue

Ovsyannikov, Ivan, MS57, 9:00 Tue

PPadberg-Gehle, Kathrin, MS103, 1:30 Wed

Padberg-Gehle, Kathrin, MS124, 1:30 Thu

Paley, Derek A., MS37, 1:15 Mon

Palmer, Cody, PP1, 8:30 Tue

Panfilov, Alexander, MS73, 4:30 Tue

Park, Paul, CP17, 5:25 Mon

Park, Youngmin, PP1, 8:30 Tue

Parlitz, Ulrich, CP2, 6:10 Sun

Parlitz, Ulrich, MS61, 1:30 Tue

Pasqualetti, Fabio, MS89, 9:30 Wed

Patel, Mainak, MS51, 10:00 Tue

Paul, Mark, MS99, 3:00 Wed

Pazó, Diego, MS129, 2:00 Thu

Peckham, Bruce B., CP17, 5:05 Mon

Pecora, Louis M., MT1, 2:00 Sun

Pecora, Louis M., MS20, 9:00 Mon

Pelinovsky, Dmitry, MS83, 10:00 Wed

Pereira, Tiago, MS27, 10:00 Mon

Petrovskii, Sergei, MS123, 1:30 Thu

Picardo, Jason R., CP1, 6:10 Sun

Pikovsky, Arkady, MS117, 8:30 Thu



Pillai, Dipin S., CP25, 4:05 Mon

Piltz, Sofia, MS87, 10:00 Wed

Pina, Jason E., PP2, 8:30 Wed

Pisarchik, Alexander N., MS31, 9:30 Mon

Plum, Michael, MS128, 3:00 Thu

Poignard, Camille, CP2, 4:50 Sun

Politi, Antonio, MS72, 4:00 Tue

Poll, Daniel, PP1, 8:30 Tue

Poon, Philip, CP6, 6:10 Sun

Porfiri, Maurizio, MS12, 9:00 Sun

Porfiri, Maurizio, MS30, 8:30 Mon

Porfiri, Maurizio, MS30, 8:30 Mon

Porter, Jeff, CP24, 3:45 Mon

NNagel, Rainer, MS47, 9:00 Tue

Naik, Shibabrat, CP6, 5:30 Sun

Nakagaki, Toshiyuki, PP2, 8:30 Wed

Nakao, Hiroya, CP3, 4:50 Sun

Nanda, Vidit, MS56, 9:30 Tue

Nayak, Alok R., MS64, 2:30 Tue

Neamtu, Alexandra, MS132, 2:00 Thu

Neda, Zoltan, MS16, 3:00 Sun

Neofytou, Giannis, PP1, 8:30 Tue

Nepomnyashchy, Alexander, MS97, 4:00 Tue

Nepomnyashchy, Alexander, MS97, 5:30 Tue

Neskovic, Predrag, PD2, 12:00 Tue

Neville, Rachel, MS9, 10:30 Sun

Newby, Jay, MS94, 1:30 Wed

Newhall, Katherine, MS13, 9:00 Sun

Newhall, Katherine, MS13, 9:00 Sun

Nguyen, Hoang, MS91, 2:00 Wed

Nicola, Wilten, PP2, 8:30 Wed

Nieddu, Garrett, PP1, 8:30 Tue

Nijholt, Eddie, MS27, 8:30 Mon

Nijholt, Eddie, MS27, 8:30 Mon

Nishikawa, Takashi, MS20, 8:30 Mon

Nishikawa, Takashi, MS20, 8:30 Mon

Nitzan, Mor, MS115, 10:00 Thu

Noel, Pierre-Andre, MS5, 10:00 Mon

Norton, Kerri-Ann, MS38, 2:45 Mon

Nykamp, Duane, MS66, 2:30 Tue

OOber-Bloebaum, Sina, MS82, 9:30 Wed

Olaniyi, Samson, PP2, 8:30 Wed

Olivar Tost, Gerard, CP26, 4:40 Tue

Olmos, Daniel, MS93, 3:00 Wed

Onozaki, Kaori, CP17, 4:05 Mon

Orosz, Gabor, MS17, 2:00 Sun

Orosz, Gabor, MS17, 2:00 Sun

Oshanin, Gleb, MS105, 5:00 Wed

Osinga, Hinke M., MS104, 5:00 Wed

Otani, Niels, MS93, 1:30 Wed

Ott, Edward, MS58, 2:30 Tue

McKinley, Scott, MS13, 10:00 Sun

Mcquighan, Kelly, MS70, 1:30 Tue

Mcquighan, Kelly, MS77, 4:00 Tue

Mcquighan, Kelly, MS122, 9:30 Thu

Medeiros, Everton S., PP1, 8:30 Tue

Meerman, Corine J., PP2, 8:30 Wed

Mehlig, Bernhard, MS35, 1:15 Mon

Mehlig, Bernhard, MS35, 1:15 Mon

Meiss, James D., CP17, 4:45 Mon

Mendoza, Joshua, PP1, 8:30 Tue

Merrison-Hort, Robert, MS114, 9:00 Thu

Metcalfe, Guy, MS26, 9:00 Mon

Meyer, Evgeny, MS10, 10:00 Sun

Mezic, Igor, MS47, 8:30 Tue


Mezic, Igor, PD2, 12:00 Tue


Mier-y-Teran, Luis, CP8, 5:30 Sun

Mier-y-Teran, Luis, MS71, 4:00 Tue

Mireles James, Jason, MS108, 4:30 Wed

Mireles-James, Jason, MS128, 1:30 Thu

Mitchell, Kevin A., MS86, 8:30 Wed



Moehlis, Jeff, IP6, 11:15 Thu

Moehlis, Jeff, MS109, 4:00 Wed

Mohapatra, Anushaya, CP21, 4:45 Mon

Mohr, Ryan, MS47, 9:30 Tue

Molkov, Yaroslav, PP2, 8:30 Wed

Moore, Richard O., MT2, 4:00 Wed

Morales Morales, Jose Eduardo, CP2, 5:50 Sun

Morone, Uriel I., MS61, 2:30 Tue

Morrison, P. J., MS24, 8:30 Mon

Motta, Francis C., MS9, 10:00 Sun

Motter, Adilson E., IP1, 11:45 Sun

Mugler, Andrew, MS46, 9:00 Tue

Munsky, Brian, MS46, 9:30 Tue

Murthy, Abhishek, CP11, 4:30 Sun

Muthusamy, Lakshmanan, CP13, 5:30 Sun

Mutua, Jones M., PP1, 8:30 Tue



SSacré, Pierre, CP27, 5:40 Tue

Sadeghpour, Mehdi, CP22, 4:05 Mon

Salih, Rizgar, CP17, 3:45 Mon

Sander, Evelyn, MS57, 10:00 Tue

Sanders, David P., CP15, 4:45 Mon

Sandstede, Bjorn, MS1, 10:30 Sun

Sandstede, Bjorn, PD1, 7:00 Mon

Sanz-Alonso, Daniel, MS61, 2:00 Tue

Sapsis, Themistoklis, MS32, 1:45 Mon

Sarma, Sridevi, MS109, 5:00 Wed

Sato, Daisuke, MS126, 1:30 Thu

Sato, Yuzuru, MS48, 9:00 Tue

Sattari, Sulimon, PP1, 8:30 Tue

Sauer, Timothy, MS15, 2:00 Sun

Sayadi, Taraneh, MS55, 9:30 Tue

Schecter, Stephen, MS122, 9:00 Thu

Scheel, Arnd, MS77, 4:00 Tue

Schelter, Björn, MS115, 9:00 Thu

Schiff, Steven J., MS109, 4:30 Wed

Schmitt, Karl, CP25, 5:05 Mon

Schumann-Bischoff, Jan, MS61, 3:00 Tue

Schwabedal, Justus T., MS50, 8:30 Tue

Schwartz, Elissa, MS98, 3:00 Wed

Schwartz, Ira B., MS33, 1:15 Mon

Schwartz, Ira B., MS33, 1:15 Mon

Schwarz, Michael, PP2, 8:30 Wed

Selvaraj, Prashanth, CP27, 4:20 Tue

Sendina Nadal, Irene, MS68, 1:30 Tue

Sendina Nadal, Irene, MS68, 3:00 Tue

Seo, Gunog, CP6, 4:50 Sun

Serrano, Sergio, MS119, 1:30 Wed

Sewalt, Lotte, MS123, 2:00 Thu

Shai, Saray, MS102, 2:30 Wed

Shaw, Leah, MS33, 1:45 Mon

Shea-Brown, Eric, MS74, 5:00 Tue

Sheombarsing, Ray, PP1, 8:30 Tue

Shiferaw, Yohannes, MS126, 2:00 Thu

Shilnikov, Andrey, MS116, 10:30 Sun

Shipman, Patrick, MS9, 9:00 Sun

Shirin, Afroza, CP28, 4:00 Tue

Roberts, Andrew, MS49, 8:30 Tue

Roberts, Andrew, MS49, 8:30 Tue

Roberts, Anthony J., MS110, 8:30 Thu

Roberts, Anthony J., MS110, 8:30 Thu

Roberts, Kerry-Lyn, MS116, 9:00 Sun

Roberts, Kerry-Lyn, MS116, 9:30 Sun

Roberts, Lewis G., MS107, 4:00 Wed

Roberts, Lewis G., MS107, 4:00 Wed

Rodriguez, Jairo, MS93, 2:30 Wed

Rodriguez, Marcos, MS50, 8:30 Tue

Rodriguez, Marcos, MS50, 8:30 Tue

Rodriguez-Bunn, Nancy, MS29, 9:30 Mon

Rohloff, Martin, MS53, 9:00 Tue

Romance, Miguel, MS68, 1:30 Tue

Romano, David, MS14, 3:00 Sun

Romeo, Francesco, MS32, 2:15 Mon

Roque, Antonio C., MS72, 5:30 Tue

Rosa, Epaminondas, MS59, 1:30 Tue



Rosado Linares, Jesus, MS29, 10:00 Mon

Rosato, Anthony, MS39, 1:15 Mon

Rosato, Anthony, MS52, 8:30 Tue

Rosenblum, Michael, MS115, 8:30 Thu



Ross, Shane D., CP6, 5:50 Sun

Rottschafer, Vivi, MS123, 1:30 Thu

Rowley, Clarence, MS60, 1:30 Tue

Roy, Rajarshi, MS28, 9:30 Mon

Roy, Ranadhir, MS97, 5:00 Tue

Roy, Subhradeep, PP2, 8:30 Wed

Rubchinsky, Leonid, MS114, 8:30 Thu

Rubchinsky, Leonid, MS114, 8:30 Thu

Rubin, Jonathan E., MS118, 8:30 Thu



Rucklidge, Alastair M., PP1, 8:30 Tue

Ruzzene, Massimo, PD2, 12:00 Tue

Ryzhov, Evgeny, PP2, 8:30 Wed

Porter, Mason A., MT1, 2:00 Sun

Pozo, Roldan, MS102, 2:00 Wed

Pratt, Larry, MS26, 9:30 Mon

Proctor, Joshua L., MS42, 2:15 Mon

Promislow, Keith, MS1, 9:00 Sun

Promislow, Keith, MS19, 8:30 Mon

Prykarpatski, Anatolij, MS39, 1:45 Mon

Putelat, Thibaut, MS121, 8:30 Thu

Putkaradze, Vakhtang, MS22, 8:30 Mon

Putkaradze, Vakhtang, MS22, 9:00 Mon

QQian, Yuzhou, PP2, 8:30 Wed

Qiu, Siwei, MS66, 1:30 Tue

Quail, Thomas D., MS73, 5:00 Tue

Queirolo, Elena, PP1, 8:30 Tue

Quininao, Cristobal, MS74, 5:30 Tue

Quinn, D Dane, MS133, 1:30 Thu

RRachinskiy, Dmitry, MS23, 9:00 Sun

Rachinskiy, Dmitry, MS23, 9:00 Sun

Rademacher, Jens, MS77, 4:30 Tue

Radons, Gunter, MS10, 9:30 Sun

Radunskaya, Ami, MS34, 1:15 Mon

Rahman, Aminur, MS39, 2:15 Mon

Reagan, Andrew, MS63, 3:00 Tue

Recupero, Vincenzo, MS78, 9:00 Wed

Redner, Sidney, MS105, 4:00 Wed

Redner, Sidney, MS105, 5:30 Wed

Reimbayev, Reimbay, PP1, 8:30 Tue

Reinhardt, Christian P., MS128, 1:30 Thu

Reinhardt, Christian P., MS128, 1:30 Thu

Renson, Ludovic, MS121, 9:30 Thu

Restrepo, Juan G., MS117, 10:00 Thu

Ribeiro, Ruy M., MS98, 1:30 Wed

Riecke, Hermann, CP15, 4:05 Mon

Rimbert, Nikolas, MS53, 9:30 Tue

Rink, Bob, MS27, 8:30 Mon

Ritchie, Paul, MS104, 4:30 Wed

Roberts, Andrew, MS36, 1:15 Mon



Teruel, Antonio E., MS118, 10:00 Thu

Thamara Kunnathu, Shajahan, MS64, 1:30 Tue

Thamara Kunnathu, Shajahan, MS64, 1:30 Tue

Thiffeault, Jean-Luc, MS111, 8:30 Thu



Thomas, Jim, MS8, 9:30 Sun

Tiedje, Tom, MS113, 10:00 Thu

Tikhomirov, Sergey, MS23, 10:30 Sun

Timme, Marc, MS54, 9:30 Tue

Timme, Marc, MS115, 8:30 Thu

Timme, Marc, MS127, 1:30 Thu

Titus, Mathew, CP15, 5:05 Mon

Toenjes, Ralf, MS76, 4:00 Tue

Toenjes, Ralf, MS76, 5:30 Tue

Topaz, Chad M., MS40, 2:45 Mon

Toroczkai, Zoltan, MS16, 3:30 Sun

Touboul, Jonathan D., MS66, 1:30 Tue

Touboul, Jonathan D., MS74, 4:00 Tue

Touboul, Jonathan D., PP2, 8:30 Wed

Treitman, Yosef M., PP2, 8:30 Wed

Tricoche, Xavier M., MS52, 9:30 Tue

Tsai, Richard, MS69, 3:00 Tue

Tsimring, Lev S., MS17, 3:00 Sun

Tu, Jonathan H., MS42, 1:15 Mon

Tu, Jonathan H., MS42, 1:15 Mon

Tu, Jonathan H., MS55, 8:30 Tue

Turitsyn, Konstantin, MS107, 5:30 Wed

Tutberidze, Mikheil, CP20, 4:25 Mon

Tzella, Alexandra, MS86, 9:00 Wed

Tzou, Justin C., MS18, 2:30 Sun

Tzou, Justin C., MS81, 8:30 Wed

Tzou, Justin C., MS94, 1:30 Wed

UUeda, Kei-Ichi, CP20, 4:45 Mon

Ullah, Ghanim, MS15, 3:30 Sun

Ulusoy, Suleyman, CP7, 4:50 Sun

Uminsky, David T., MS11, 10:00 Sun

Uzelac, Ilija, MS126, 3:00 Thu

Stremler, Mark A., MS79, 8:30 Wed



Strickland, Christopher, MS9, 9:00 Sun

Strickland, Christopher, MS9, 9:00 Sun

Strogatz, Steven H., CP18, 3:45 Mon

Stuart, Andrew, IP3, 6:00 Mon

Sturman, Rob, PP2, 8:30 Wed

Sudakov, Ivan, MS113, 8:30 Thu

Sudakov, Ivan, MS113, 8:30 Thu

Suetani, Hiromichi, MS101, 2:30 Wed

Sukhinin, Alexey, CP2, 5:10 Sun

Sun, Jie, MS5, 8:30 Mon

Susuki, Yoshihiko, MS47, 8:30 Tue



Szalai, Robert, MS10, 9:00 Sun

Szalai, Robert, MS121, 8:30 Thu

Szalai, Robert, MS133, 1:30 Thu

Szezech Jr, Jose D., PP1, 8:30 Tue

Szmolyan, Peter, CP18, 4:45 Mon

Szwaykowska, Klementyna, MS71, 4:00 Tue

Szwaykowska, Klementyna, MS71, 5:30 Tue

TTaira, Kunihiko, MS55, 8:30 Tue

Talon, Laurent, MS86, 10:00 Wed

Tang, Wenbo, MS3, 10:00 Sun

Tanwani, Aneel, MS78, 10:00 Wed

Tao, Molei, MS82, 8:30 Wed



Taylor, Dane, MS9, 9:30 Sun

Taylor, Dane, MS5, 8:30 Mon

Taylor-King, Jake P., PP2, 8:30 Wed

Teitsworth, Stephen, MS28, 10:00 Mon

Tel, Tamas, MS58, 1:30 Tue

Teramoto, Takashi, PP1, 8:30 Tue

Teramura, Toshiki, PP1, 8:30 Tue

Terra, Maisa O., MS108, 5:30 Wed

Shlizeman, Eli, MS7, 10:30 Sun

Short, Martin, MS88, 8:30 Wed

Showalter, Kenneth, MS76, 5:00 Tue

Sieber, Jan, MS106, 4:30 Wed

Siero, Eric, MS123, 2:30 Thu

Signerska, Justyna H., PP2, 8:30 Wed

Simpson, David J., MS87, 8:30 Wed



Sinitsyn, Nikolai, MS46, 10:00 Tue

Sipahi, Rifat, MS12, 10:30 Sun

Sivasankaran, Anoop, PP1, 8:30 Tue

Slawik, Alexander, CP23, 5:05 Mon

Slivinski, Laura, MS63, 1:30 Tue

Slivinski, Laura, MS63, 1:30 Tue

So, Paul, MS117, 8:30 Thu



Solomon, Thomas H., MS26, 8:30 Mon

Solomon, Thomas H., MS86, 8:30 Wed

Solomon, Thomas H., MS99, 1:30 Wed

Sommerlade, Linda, CP27, 5:00 Tue

Sorrentino, Francesco, MS20, 8:30 Mon

Sorrentino, Francesco, MS20, 9:30 Mon

Speetjens, Michel, MS26, 8:30 Mon

Speetjens, Michel, MS26, 10:00 Mon

Spiller, Elaine, MS21, 9:00 Mon

Spinello, Davide, MS30, 9:00 Mon

Sridhar, S, MS64, 3:00 Tue

Stanton, Samuel, PD2, 12:00 Tue

Starke, Jens, MS40, 2:15 Mon

Starosvetsky, Yuli, MS45, 10:00 Tue

Starosvetsky, Yuli, MS83, 8:30 Wed

Starosvetsky, Yuli, MS96, 1:30 Wed

Steinbock, Oliver, MS73, 5:30 Tue

Steiner, Paul, MS38, 2:15 Mon

Stepan, Gabor, MS10, 9:00 Sun

Stepan, Gabor, MS10, 10:30 Sun

Stephen Tladi, Maleafisha, CP12, 5:50 Sun

Stoica, Cristina, MS79, 9:00 Wed



VVaidya, Naveen K., MS85, 8:30 Wed

Vaidya, Naveen K., MS98, 1:30 Wed

Vaidya, Naveen K., MS98, 2:30 Wed

Vaidya, Umesh, MS131, 2:00 Thu

Vainchtein, Anna, MS83, 8:30 Wed

Vainchtein, Anna, MS96, 1:30 Wed

Vainchtein, Dmitri, MS26, 8:30 Mon

Vainchtein, Dmitri, MS32, 2:45 Mon

Vakakis, Alexander, MS32, 1:15 Mon

Vakakis, Alexander, MS45, 8:30 Tue

Vakakis, Alexander, MS45, 8:30 Tue

Van Den Berg, Jan Bouwe, MS56, 8:30 Tue

Van Den Berg, Jan Bouwe, MS128, 2:00 Thu

van Heijster, Peter, CP1, 4:30 Sun

van Heijster, Peter, MS70, 1:30 Tue

van Heijster, Peter, MS77, 4:00 Tue

Vandervorst, Robert, MS56, 8:30 Tue

Vanneste, Jacques, MS8, 10:30 Sun

Varkonyi, Peter L., MS121, 9:00 Thu

Vasudevan, Ram, MS131, 1:30 Thu

Vasudevan, Ram, MS131, 3:00 Thu

Veerman, Frits, CP20, 5:05 Mon

Veliz-Cuba, Alan, MS66, 2:00 Tue

Venel, Juliette, MS91, 1:30 Wed

Verschueren Van Rees, Nicolas, MS18, 3:30 Sun

Vincze, Miklos P., CP12, 4:50 Sun

Virgin, Lawrie N., CP25, 3:45 Mon

Virkar, Yogesh, CP16, 4:05 Mon

Vlajic, Nicholas, MS121, 10:00 Thu

Vo, Theodore, MS116, 9:00 Sun

Vo, Theodore, MS116, 9:00 Sun

Volkening, Alexandria, MS40, 1:15 Mon

Volkening, Alexandria, MS40, 1:15 Mon

Vollmer, Jürgen, MS53, 8:30 Tue

Vollmer, Jürgen, MS53, 8:30 Tue

Volper, Vladimir, MS97, 4:00 Tue

von Brecht, James, MS88, 9:00 Wed

WWackerbauer, Renate A., CP16, 4:25 Mon

Wagner, Till, MS113, 9:30 Thu

Wang, Kun, CP7, 5:10 Sun

Wang, Wei, MS120, 9:30 Thu

Wang, Xiaosun, MS133, 2:00 Thu

Wang, Xueying, CP27, 4:00 Tue

Wang, Yangyang, MS25, 9:00 Mon

Wang, Yu V., CP20, 3:45 Mon

Wang, Zhen, MS68, 1:30 Tue

Wang, Zhen, MS68, 2:00 Tue

Wang, Zhen, PP1, 8:30 Tue

Warchall, Henry, PD2, 12:00 Tue

Ward, Michael, MS18, 3:00 Sun

Ward, Thomas, CP7, 5:30 Sun

Wares, Joanna, MS34, 1:15 Mon

Watanabe, Shinya, PP2, 8:30 Wed

Watson, Scott T., CP16, 5:05 Mon

Webb, Glenn, MS34, 2:15 Mon

Wechselberger, Martin, MS77, 5:30 Tue

Wells, Daniel, CP16, 3:45 Mon

Welsh, Andrea J., MS28, 8:30 Mon

Welsh, Andrea J., CP16, 4:45 Mon

Whitehead, Jared P., MS8, 9:00 Sun

Wickramasinghe, B.M. Shandeepa D., PP1, 8:30 Tue

Widiasih, Esther, MS36, 1:15 Mon

Widiasih, Esther, MS36, 1:45 Mon

Widiasih, Esther, MS49, 8:30 Tue

Wieczorek, Sebastian M., MS104, 4:00 Wed

Wieczorek, Sebastian M., MS104, 4:00 Wed

Wiercigroch, Marian, MS100, 2:30 Wed

Williams, Matthew O., MS60, 2:00 Tue

Wilson, Dan D., MS109, 4:00 Wed

Wilson, Dan D., MS109, 4:00 Wed

Wodarz, Dominik, MS34, 2:45 Mon

Wojcik, Jeremy, MS50, 9:30 Tue

Wojcik, Jeremy, PP2, 8:30 Wed

Worthington, Joachim, PP1, 8:30 Tue

Wu, Hao, MS52, 9:00 Tue

Wu, Qiliang, MS19, 8:30 Mon

Wurm, Alexander, MS24, 8:30 Mon

Wurm, Alexander, MS24, 8:30 Mon

Wyller, John, MS84, 9:00 Wed

XXia, Chao, PP2, 8:30 Wed

Xie, Shuangquan, MS94, 3:00 Wed

Xing, Tingli, PP1, 8:30 Tue

Xu, Bin, PP2, 8:30 Wed

Xu, Mu, CP25, 4:25 Mon

YYanao, Tomohiro, MS95, 2:30 Wed

Yanchuk, Serhiy, MS106, 4:00 Wed

Yang, Dennis, MS84, 8:30 Wed

Yang, Dennis, MS84, 8:30 Wed

Yang, Jinkyu, MS83, 8:30 Wed

Ye, Jingxin, MS101, 2:00 Wed

Yeaton, Isaac, CP25, 4:45 Mon

Yi, Yanyan, MS126, 1:30 Thu

Yochelis, Arik, MS18, 2:00 Sun

Yochelis, Arik, MS18, 2:00 Sun

Yoshimura, Hiroaki, MS4, 9:00 Sun

Young, Alexander L., PP2, 8:30 Wed

Young, Glenn S., PP1, 8:30 Tue

Young, Lai-Sang, MS58, 2:00 Tue

Youngs, Nora, MS14, 3:30 Sun

ZZakharova, Anna, MS59, 3:00 Tue

Zaks, Michael A., MS59, 2:00 Tue

Zavitz, Daniel R., PP1, 8:30 Tue

Zelnik, Yuval, CP12, 4:30 Sun

Zenkov, Dmitry, MS4, 9:00 Sun

Zenkov, Dmitry, MS22, 10:00 Mon

Zhang, Calvin, CP27, 5:20 Tue

Zhang, Fumin, MS3, 9:30 Sun

Zhang, Yijing, MS96, 2:30 Wed

Zhang, Zhihui, CP20, 4:05 Mon

Zhao, Lihong, CP27, 4:40 Tue

Zhou, Douglas, MS7, 9:00 Sun

Zhou, Douglas, MS7, 10:00 Sun

Zhu, Xueyu, MS90, 9:00 Wed



Zhuzhoma, Evgeny, PP2, 8:30 Wed

Zlotnik, Anatoly, MS30, 10:00 Mon

Zochowski, Michal, MS127, 3:00 Thu

Zykov, Vladimir, MS93, 2:00 Wed



Notes


DS15 Budget

Conference BudgetSIAM Conference on Dynamical SystemsMay 17 - 21, 2015Snowbird, UT

Expected Paid Attendance 780

RevenueRegistration Income $223,355

Total $223,355

ExpensesPrinting $9,200Organizing Committee $6,500Invited Speakers $20,000Food and Beverage $35,800AV Equipment and Telecommunication $10,800Advertising $7,000Conference Labor (including benefits) $56,846Other (supplies, staff travel, freight, misc.) $19,400Administrative $18,578Accounting/Distribution & Shipping $9,907Information Systems $17,862Customer Service $6,747Marketing $10,597Office Space (Building) $6,703Other SIAM Services $7,079

Total $243,019

Net Conference Expense ($19,664)

Support Provided by SIAM $19,664$0

Estimated Support for Travel Awards not included above:

Early Career and Students 67 $50,550


Snowbird Ski and Summer Resort, Hotel Floor Plan

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SnowbirdCliff LodgeLevel C

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