POSTER SESSION · O. Vazquez-Candanedo and F. M. Izrailev Instituto de Física, Universidad...

POSTER SESSION

FEBRUARY 21, 18:30 – 20:00 HRS. (Salón Verde, Edificio Carolino)

PARTICIPANT TITLE OF THE POSTER Danila F. Tavares and R. N. Costa Filho Departamento de Física, Universidade Federal do Ceará, Brazil

NON-UNIFORM DRAG FORCE ON THE FERMI ACCELERATOR MODEL

Rodrigo Toledo Hernández1 y Pablo Padilla Longoria2

1)Centro de Ciencias de la Complejidad (C3), CONACyT-UNAM, Torre de Ingeniería 6to. piso, CU; México D.F. 2)Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS), UNAM, CU; México, D.F.

DINÁMICA DEL CÁNCER Y TEORÍA DE JUEGOS: UN MODELO EXTENDIDO

ESPACIALMENTE

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov Benemérita Universidad Autónoma de Puebla, Puebla, México

ANDERSON LOCALIZATION IN IDEAL METAMATERIALS

WITH RANDOM REFRACTION INDEX

V. M. Rodríguez and M. G. Cosenza Centro de Física Fundamental Universidad de Los Andes Mérida, Venezuela

AMPLITUDE DEATH IN GLOBALLY COUPLED CHAOTIC SYSTEMS WITH

DELAY

Juliano A. de Oliveira and Edson D. Leonel DEMAC and IGCE Universidade Estadual Paulista - Rio Claro- SP – Brazil

CRITICAL EXPONENTS VIA LOCALISATION OF INVARIANT SPANNING

CURVE FOR A FAMILY OF HAMILTONIAN SYSTEMS

Juliano A. de Oliveira and Edson D. Leonel DEMAC and IGCE Universidade Estadual Paulista - Rio Claro- SP – Brazil

THE CONSEQUENCES OF WEAK DISSIPATION IN A FAMILY OF

TWODIMENSIONAL MAPPING

O. Vazquez-Candanedo and F. M. Izrailev Instituto de Física, Universidad Autónoma de Puebla, Puebla, México

ANDERSON LOCALIZATION IN BI-LAYER DISORDERED ARRAYS WITH

ABSORPTION AND GAIN

María del Carmen Pérez Zarate, UACM, México

Alejandro López Malvez, ESCOM, México Pablo Padilla Longoria, IIMAS, UNAM, D.F. México

STEM CELL DYNAMICS OF THE ROOT MERISTEM NICHE

IN ARABIDOPSIS THALIANA.

L. I. Ledesma Fosados (1), V. González Dávila (2), J. A. Betancourt Mar (1) , E. J. Suárez Domínguez (1) (1) Mexican Institute of Complex Systems. Tlaxcala 111 Col. Unidad Nacional, C.P. 89410, Cd. Madero, Tamps. México. (2) Geo-Estratos S.A. de C.V, Calle 7 No 205-1, Col. Jardín 20 de Noviembre, C.P. 89440, Cd. Madero, Tamps. México.

STABILITY OF INJECTION BRINE MIXTURES

Abraham Villatoro Tello, Dr. Fernando Reyes Cortés Facultad de Ciencias De La Electrónica, BUAP, Puebla, México.

ADAPTATIVE CONTROL OF ROBOT MANIPULATORS

L. Vargas Martínez, Dr. F. Reyes. Grupo de robótica, FCE-BUAP, Apdo. Postal 62-570, Av. San Claudio y 14 Sur, 72570, Puebla, Puebla, México.

ROBOTIC’S EXPERIMENTAL PLATAFORMA

Tiago Botari Departamento de Física, Universidade Estadual Paulista,UNESP, Rio Claro - São Paulo, Brazil

Edson Denis Leonel DEMAC and IGCE Universidade Estadual Paulista - Rio Claro- SP – Brazil

DYNAMICAL PROPERTIES OF A FERMI-

ULAM MODEL WITH EXTERNAL PERTURBATION OF VAN DER POL TYPE

M.A. Limón-Díaz and F. Reyes-Cortés Facultad de Ciencias de la Electrónica, BUAP, Puebla, Puebla, México

EVALUATION OF FORCE CONTROL STRATEGIES FOR ROBOT

MANIPULATORS

R. Sevilla-Escoboza (1), Massimiliano Zanin (3) , R. Jaimes-Reategui (1), G. Huerta-Cuellar (1), A. N. Pisarchik (2), J. H. García-López (1) (1) Centro Universitario de Los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseo de la Montaña, Las de Moreno, Jalisco, México (2)Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, León, México. (3) Universidad Autónoma de Madrid, 28049 Madrid, España

SYNCHRONIZATION ATTACK OF CHAOTIC COMMUNICATION SYSTEMS

G. Huerta-Cuellar (1), R. Jaimes-Reategui (1), R. Sevilla-Escoboza (1), A. N. Pisarchik (2), J. H. García-López (1), C. E. Castañeda-Hernandez (1), and D. Lopez Mancilla (1) (1) Centro Universitario de Los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseo de la Montaña, Las de Moreno, Jalisco, México (2) Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, León, México

NONLINEAR OPTICAL SYNAPSE

R. Jaimes-Reategui (1), R. Sevilla-Escoboza (1), G. Huerta-Cuellar (1)1, A. N. Pisarchik (2), J. H. García-López (1), D. Lopez Mancilla (1) and C. E. Castañeda-Hernandez (1) (1) Centro Universitario de Los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseo de la Montaña, Las de Moreno, Jalisco, México (2) Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, León, México

ROGUE WAVES IN A MULTISTABLE FIBER LASER

André L. P. Livorati¹, Carl P. Dettmann², and Edson. D. Leonel³ ¹ IFUSP - Univ. de São Paulo - USP - SP - Brazil ² Univ. of Bristol - England ³ DEMAC - Univ. Estadual Paulista - UNESP - SP – Brazil

ON DYNAMICS AND STATISTICS OF A CONSERVATIVE BOUNCER

MODEL: ACCELERATOR AND DECELERATOR MODES

Roberto Álvarez-Martínez Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México (UNAM),D.F. México

EVOLUTION OF RNA VIRUSES WITH FREQUENCY-DEPENDENT

SELECTION.

David P. Sanders Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México Thomas Gilbert (1), Huu Chuong Nguyen (1) & *David P. Sanders* (2) (1) Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, C. P. 231, Campus Plaine, B-1050 Brussels, Belgium (2) Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México DF, Mexico

DIFFUSIVE PROPERTIES OF LORENTZ GASES VIA PERSISTENT RANDOM WALKS

Francisco J. Martínez IIMAS, UNAM, D.F. México

NORMAL MODES OF 1-D ELASTIC NETWORKS

Non-Uniform Drag Force on the Fermi Accelerator Model

Danila F. Tavares∗ and R. N. Costa Filho†

Departamento de F́ısica, Universidade Federal do Ceará,

Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

Edson D. Leonel‡

Departamento de Estat́ıstica, Matemática Aplicada e Computação – UNESP–Universidade Estadual Paulista

Av. 24A, 1515 – CEP: 13506-900 – Rio Claro – SP – Brazil

(Dated: January 25, 2012)

Some dynamical properties for a particle suffering the action of a generic drag force are obtainedfor a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force,like a gas and is assumed to be proportional to any power of the velocity F ∝ −ηV γ . The dynamicsis described by a two dimensional nonlinear area-contracting mapping obtained via the solution ofthe second Newton’s law of motion. We prove analytically that the decay of high energy is given bya continued fraction which recovers the following expressions: (i) linear for γ = 1; (ii) exponentialfor γ = 2 and (iii) second degree polynomial type for γ = 1.5. For any value of γ 6= 1, and γ 6= 2the numerical results shows a polynomial behavior for the velocity decay. Our results are discussedfor both the complete and simplified versions. The procedure used in the present paper can beextended to many different kinds of systems including a class of billiards problems.

∗Electronic address: [email protected]

†Electronic address: [email protected]

‡Electronic address: [email protected]

Dinámica del Cáncer y Teoŕıa de Juegos: un

modelo extendido espacialmente

Rodrigo Toledo Hernández1y Pablo Padilla Longoria2

1)Centro de Ciencias de la Complejidad (C3), CONACyT-UNAM,Torre de Ingenieŕıa 6◦piso, CU; México D.F.

2)Instituto de Investigaciones en Matemáticas Aplicadas y enSistemas (IIMAS), UNAM, CU; México, D.F.

Abstract

Las aplicaciones de la teoŕıa de juegos evolutiva (TJE) permean todaslas áreas de la bioloǵıa. Algunas ideas de mecanismos evolutivos puedenser formuladas en términos de ecuaciones matemáticas. La adecuaciónen la Teoŕıa Darwiniana puede depender de la abundancia relativa defenotipos dentro de las poblaciones (selección dependiente de la frecuen-cia). Este tipo de selección natural es descrito por la ecuación replicadorade la TJE entre n diferentes fenotipos en una población infinitamentegrande, bien mezclada y sin mutaciones, por lo tanto es una herramientamatemática apropiada para investigar estos sucesos.

dxidt

= xi[f(~x) − φ(~x)] (1)

para i = 1, 2, . . . , N donde xi= frecuencia del tipo i, f(~xi) =∑N

1aij( ~xj)

es la función de adecuación y φ(~xi) =∑N

1f(~xi)xi la adecuación promedio.

Por otro lado se puede argumentar en su contra que los efectos estocásticosy espaciales son ignorados siendo que éstos tienen un papel importante enlos sistemas biológicos. “Bien mezclados” significa que la estructura espa-cial de la población es ignorada y que todos los individuos tienen la mismaprobabilidad de interactuar con cualquier otro. En el presente trabajo seincorporan expĺıcitamente aspectos de la estructura espacial del fenómenomediante su vecindad inmediata, aśı como su naturaleza dinámica. Se usala ecuación replicadora para modelar la invasión de células de MielomaMúltiple al hueso, utilizando un juego de tres jugadores. Por lo que laecuación se modifica de la forma:

dxijidt

= xiji [fij(~x) − Φij(~x)] (2)

donde Φij = 15

∑51fvi es el paramétro que acopla espacialmente a las

poblaciones. Se presenta el modelo y resultados tanto anaĺıticos comonuméricos.

Conceptos clave: Teoŕıa de Juegos Evolutiva, Ecuación Replicadora,cáncer, Mieloma Múltiple.

Referencias:1) Nowak M, et al.(2004); Evolutionary Dynamics of Bi-ological Games, Science 303:793. 2) Nowak M.; Ohtsuki H.(2006); Thereplicator equation on graphs, J Theor Biol. 243(1): 86–97.

1

Anderson Localization in Ideal Metamaterials with Random Refraction Index

E. J. Torres-Herrera, F. M. Izrailev, and N. M. MakarovBenemérita Universidad Autónoma de Puebla,

Puebla, Pue., 72050, México E-mail [email protected]

We consider one-dimensional periodic-on-average bi-layered structures with weak randomness in refraction index (compositional disorder) of basic, a and b , slabs composing the unit-cell. Main attention is paid to the comparison of two systems: the homogeneous stack when both slabs are made from right-handed (RH) optic materials, and mixed stack when a slabs contain RH-material while b layers are of left-handed (LH) material. The localization length L loc , which is the key parameter of Anderson localization, is derived with the Hamiltonian map method.

We show that when the thicknesses of basic layers are different, d a≠db , the localization length is described by an universal analytical expression that includes all possible correlations within a and b disorders, as well as, between them. For both homogeneous RH-RH and mixed RH-LH stack-structures, the inverse localization length obeys the conventional frequency dependence

L loc−1∝ω2 for ω 0 . (1)

This expression remains valid also for the homogeneous RH-RH stack with d a=d b . In addition, L loc vanishes at the bottom and top of spectral Bloch bands. However, specific correlations in disorders may result in anomalous ω -dependence. In particular, the localization length exhibits the Fabry-Perot resonances, resulting in its resonance increase, and consequently, in the suppression of localization. If basic slabs are matched (have equal impedances), the localization length diverges and the perfect transparency emerges, while a disorder itself persists. This conclusion is general, and does not depend on the strength of disorder.

The mixed RH-LH stack exhibits highly non-trivial properties originated from the nonuniform distribution of wave phase, even in the case of white-noise disorder. We analytically obtained that in this case the localization length diverges in the standard second-order perturbation theory. Therefore, recently numerically revealed anomalies in L loc [3] are due to the fourth order in disorder. Our further study confirmed this expectation and showed that the correct limit has the following form

L loc−1∝ω8 for ω 0 , (2)

and not L loc−1∝ω6 as is claimed in Ref. [3]. Our numerical data manifest excellent agreement

with the analytical results.

[1] F.M. Izrailev, N.M. Makarov, E.J. Torres-Herrera, Physica B 405, 3022 (2010). [2] E.J. Torres-Herrera, F.M. Izrailev, N.M. Makarov, Low Temp. Phys. 37, 1201 (2011). [3] A.A. Asatryan et al., Phys. Rev. Lett. 99, 193902 (2007); Phys. Rev. B 81, 075124 (2010). [4] E.J. Torres-Herrera, F.M. Izrailev, N.M. Makarov, (2012), to appear.

AMPLITUDE DEATH IN GLOBALLY COUPLED CHAOTIC SYSTEMS WITH DELAY.

V. M. Rodríguez and M. G. Cosenza

Centro de Física Fundamental

Universidad de Los Andes

Mérida, Venezuela

Email: [email protected]

The phenomenon of amplitude death refers to a situation where individual oscillators cease oscillating and become synchronized in a fixed point state when they are coupled. In this work we investigate the emergence of amplitude death in systems of chaotic oscillators, such as Rössler and Lorentz, subject to a global interaction with a time delay. The appearance of synchronization in general, as well as the phenomenon of amplitude death are studied on the space of parameters of the system, given by the strength of the coupling and the amount of time delay. The regions of parameters where amplitude death emerges on this space exhibit a complex structure, such as islands of synchronization and islands of death. We have uncovered two distinct scenarios for the occurrence of amplitude death: (i) synchronization and amplitude death occur simultaneously, and (ii) synchronization precedes amplitude death. We identify the conditions for the occurrence of both scenarios and propose a simple geometric interpretation for them.

CRITICAL EXPONENTS VIA LOCALISATION OF INVARIANT SPANNING CURVE FOR A FAMILY OF HAMILTONIAN SYSTEMS

Juliano A. de Oliveira and Edson D. Leonel

DEMAC and IGCE Universidade Estadual Paulista - Rio Claro- SP - Brazil


Critical exponents that describe a transition from integrability to non-integrability in a two-dimensional, nonlinear and area preserving map are obtained via localization of the first invariant spanning curve in the phase space. In a general class of systems the position of the first invariant tori is estimated by reducing the mapping of the system to the standard mapping where a transition takes place from local to global chaos. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori whose position of the first of them depends on the control parameters. The formalism leads us to obtain analytically critical exponents that describe the behavior of the average variable (action) along the chaotic sea. The result is compared to several models in the literature confirming the approach is of large interest. The formalism used is general and the procedure can be extended to many other different systems.

THE CONSEQUENCES OF WEAK DISSIPATION IN A FAMILY OF TWO-DIMENSIONAL MAPPING

Juliano A. de Oliveira and Edson D. Leonel

DEMAC and IGCE

Universidade Estadual Paulista - Rio Claro- SP - Brazil


The influence of weak dissipation and its consequences in a two-dimensional mapping are studied. The mapping is parametrised by an exponent $\gamma$ in one of the dynamical variables and by a parameter $\delta$ which denotes the amount of the dissipation. It is shown that for different values of $\gamma$ the structure of the phase space of the non-dissipative model is replaced by a large number of attractors. The approach to the attracting fixed point is characterized both analytically and numerically. The attracting fixed point exhibit a very complicate basin of attraction.

ANDERSON LOCALIZATION IN BI-LAYER DISORDERED ARRAYS WITH

ABSORPTION AND GAIN

O. Vazquez-Candanedo and F. M. Izrailev

Instituto de Física, Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla, Pue., 72570, México


We study Anderson localization in a bi-layer array composed by left and right-handed materials with absorption/gain in basic slabs, and with a disorder incorporated in the structure via random dielectric constants. Our main interest is in the transport properties of such arrays as a function of frequency, and how these differ from cases without absorption/gain Ref.[1]. We also analyze whether the prediction that the inverse localization length can be expressed as a sum of two terms that separately depend on the degree of gain/absorption and disorder obtained in Ref.[2], for models with normal materials, are valid in the case of arrays with metamaterials. In the numerical approach we use standard transfer matrix methods. References: [1]E.J. Torres-Herrera, F.M. Izrailev and N.M. Makarov, Non-conventional Anderson Localization in Bi- layered Structures with Metamaterials, (2011). [2]Z.Q. Zhang, Phys. Rev. B, 52, 7960 (1995).

STEM CELL DYNAMICS OF THE ROOT MERISTEM NICHE

IN ARABIDOPSIS THALIANA.

María del Carmen Pérez Zarate, UACM, México

Alejandro López Malvez, ESCOM, México

Pablo Padilla Longoria, IIMAS, UNAM, D.F. México


Different studies in Arabidopsis thaliana have shown that meristems control the development

of organs in plants maintaining a balance between cell division and differentiation in the stem

cell niche.

In order to try to understand the dynamics of the root meristems, we propose a mathematical

model incorporating explicit space dependence that takes into account:

The pattern that is formed during early embryonic stages, in which the position of

meristematic cells plays a fundamental role in the determination of the corresponding

cell fate, due to both short and long range signals. The former come from neighboring

cells, while the latter are sent by mature cells from the rest of the plant and contribute

to the cell fate determination.

The quiescent center is considered as a reservoir of cells that replaces damaged cells

in the plant as well as a global organizing center of the cellular pattern.

With this model based on cellular automata and ordinary differential equations we intend to

show that the geometry and architecture of the root are coupled with the cell communication

processes mentioned above and that gives rise to a robust system.

STABILITY OF INJECTION BRINE MIXTURES

L. I. Ledesma Fosados (1), V. González Dávila (2),

J. A. Betancourt Mar (1) , E. J. Suárez Domínguez (1)

(1) Mexican Institute of Complex Systems. Tlaxcala 111 Col. Unidad Nacional, C.P.

89410, Cd. Madero, Tamps. México.

(2) Geo-Estratos S.A. de C.V, Calle 7 No 205-1, Col. Jardín 20 de Noviembre, C.P.

89440, Cd. Madero, Tamps. México.

Email:[email protected]

During the operation of an oil well, water is pumped to the reservoir and in this way can maintain or even increase this pressure as a whole and thereby increase the production of crude by physical displacement of the petroleum. However, the most common problem with this method is the accumulation of sediments and the formation of incrustations in the oil ducts due to the combination of ions of connate water and the water introduced, affecting the production ducts and injectors as well as the surface equipment. This represents increases in production costs, for which we have sought to predict the amount of scale in pipes. These predictions are quite limited by the number of variables that affect this system such as temperature and ion concentration as well as heterogeneity of ions present. In this work we determined the theoretical amount of precipitates from experimental data on the concentration of ions in the mixture of connate water and sea water in different percentages and determined on a gravimetric method. These results were compared with hypothetical calculations of the concentration of maximum possible precipitates and probable maximum precipitates expressed in mg / L. It was found that the experimental results at low ion concentration show a linear trend similar to the concentrations calculated at the same mixing ratio. However, by increasing the concentration of ions, the experimentally determined concentration loses its linearity.

ADAPTATIVE CONTROL OF ROBOT MANIPULATORS

Abraham Villatoro Tello, Dr. Fernando Reyes Cortés

Facultad de Ciencias De La Electrónica, BUAP,

Puebla, México.

Email: [email protected], [email protected]

In recent years, robotics has grown significantly due to advances in science such as

electronics, computers and communications. At the same time has grown the use

of control systems, which are increasingly sophisticated, as the tasks have become

more complex. This is why there is need for greater reliability and security of such

systems.

In response to these needs many proposals have emerged in the development of

controllers. Among them are the adaptive-type controllers, whose main feature is

the ease of handling the uncertainty created by changes in the system. That is,

the adaptive control is characterized by adapting to unpredictable environmental

changes, whether external or internal.

The position control of robot manipulators is a very important problem in the

industry, it can be interpreted as taking the robot from an initial position to a desired

position with the smallest error in the shortest time possible.

In this work we developed a new control structure, which was implemented in the last

link of a 3 degrees of freedom robot, which corresponds to the dynamic model of a

pendulum. We look for the tuning of the proportional gain to be automatic. This

means that the gain adjusts its values as the robot reaches the desired position.

This function was simulated for two types of controllers, and the results were very

favorable, which lead us to the next step, that is the experimental evaluation and

demonstrate Lyapunov stability.

mailto:[email protected]:[email protected]

ROBOTIC’S EXPERIMENTAL PLATAFORMA

L. Vargas Martínez, Dr. F. Reyes.

Grupo de robótica, FCE-BUAP, Apdo. Postal 62-570,

Av. San Claudio y 14 Sur, 72570, Puebla, Puebla, México.

[email protected], [email protected]

The robotic is a science is supported from various disciplines as: physic, mathematic,

electronic, control theory, the computational sciences and other. In the course of

time there’s been great progress as new control theories are proposed and as

technological advances allow, therefore, it is said that robotics is a new field of

modern technology.

This work addresses the implementation of a robot manipulator of 3 degrees of

freedom (d.o.f) as an experimental platform, this means, the mechanical part is linked

with the necessary electronics to enable the operation of the robot and software

development that allows position control under a proposed control law.

To know the physical parameters of the robot we use the method of parametric

identification based on the least squares algorithm and to validate the data was

performed a simulation of the dynamics of the robot based on the measured data

directly from the robot.

With the experimental platform we evaluate the proposed control algorithm in which was showed a good performance that allow us it o say we achieve the goal of position control. That’s the importance of this type of platforms that are used for scientific research in robotics.

mailto:[email protected]:[email protected]

DYNAMICAL PROPERTIES OF A FERMI-ULAM MODEL WITH EXTERNAL PERTURBATION OF VAN DER POL TYPE

Tiago Botari

Departamento de Física, Universidade Estadual Paulista,UNESP,

Rio Claro - São Paulo, Brasil


Edson Denis Leonel

DEMAC and IGCE

Universidade Estadual Paulista - Rio Claro- SP - Brazil


The dynamics of a classical particle of mass m confined to bounce within two rigid walls is considered. One of them is assumed to be fixed while the other one is time dependent and its position is given by a Van der Pol oscillator. Two dynamical regimes are considered: (i) the case where the moving wall is infinitely heavy and (ii) the situation where the moving wall has a finite mass. For case (i), the statistical properties of the average velocity of the particle reveals a scale invariance with respect to the control parameters. For case (ii), a scenario of dissipation is observed including attracting fixed points with a complicate basin boundary geometry.

EVALUATION OF FORCE CONTROL STRATEGIES FOR ROBOT MANIPULATORS

M.A. Limón-Díaz and F. Reyes-Cortés

Facultad de Ciencias de la Electrónica, BUAP, Puebla,

Puebla, México

Email: [email protected], [email protected]

The position and trajectory control have solved many problems in the industry, but in several industrial applications such as polishing, surface cleaning, assembly, among others, is not enough, because the robot manipulator enter in contact with the environment, generating interaction forces between the robot manipulator and the environment. The force control is a technology that has been developed to all a gap in manufacture automated processes such as machining, casting, forging, etc. This type of control allows these industrial processes to obtain the desired result. The force control is to ensure that the last link of the robot manipulator to apply a desired force level during the task of interacting with the environment. An important point to note is that a force control strategy only makes sense in those workspace directions along which there are forces of interaction between the robot manipulator and the environment. Because of this, development new structures of force control is an important contribution to the emerging needs of industry.

mailto:[email protected]

SYNCHRONIZATION ATTACK OF CHAOTIC COMMUNICATION SYSTEMS

R. Sevilla-Escoboza (1), Massimiliano Zanin (3) , R. Jaimes-Reategui (1),

G. Huerta-Cuellar (1), A. N. Pisarchik (2), J. H. García-López (1)

(1) Centro Universitario de Los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseo de la Montaña, Las de Moreno, Jalisco, México

(2)Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, León, México. (3) Universidad Autónoma de Madrid, 28049 Madrid, España


Synchronization of chaotic oscillators has an important application in cryptography. When two identical oscillators are coupled, they can b e completely synchronized and the chaotic output of the transmitter oscillator can b e used to mask a message. Although the oscillator parameters are usually used as secret keys, the sensitivity of such a cryptosystem to a parameter change has never been systematically analyzed. To cryptanalize a communication system based on synchronization of chaotic oscillators, we intro duce a synchronization attack which implies the recovering of unknown parameters by searching a minimum synchronization error. Using the synchronization attack we cryptanalize communication systems based on the Rossler and Chua chaotic oscillators. We suggest to include this attack as a standard security check for future works. Keywords: Rossler oscillator, Chua oscillator, cryptanalysis, secure communication, synchronization, chaos

NONLINEAR OPTICAL SYNAPSE

G. Huerta-Cuellar (1), R. Jaimes-Reategui (1), R. Sevilla-Escoboza (1),

A. N. Pisarchik (2), J. H. García-López (1), C. E. Castañeda-Hernandez (1), and D. Lopez Mancilla (1)


(2) Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, León, México


In this work we propose an optical synaptic sensor based on a fiber laser driven by a neural FinzHung-Nagumo electronic circuit, to connect with another neuron. The architecture of possible optical synaptic connections is described introducing different kinds of opto-electronic coupling between neurons: laser cavity loss modulation and pump laser modulation. The control parameters of the proposed optical synapse provide additional degrees of flexibility to the neuron connection traditionally controlled only by coupling strengths in artificial networks.

ROGUE WAVES IN A MULTISTABLE FIBER LASER

R. Jaimes-Reategui (1), R. Sevilla-Escoboza (1), G. Huerta-Cuellar (1)1,

A. N. Pisarchik (2), J. H. García-López (1), D. Lopez Mancilla (1), and C. E. Castañeda-Hernandez (1)


(2) Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, León, México


Clear evidence of rogue waves in a multistable system is revealed with an erbium-doped fiber laser

driven by harmonic pump modulation [1]. We demonstrate numerically and experimentally that a

low-pass noise filtering can control the probability for the appearance of a particular state. The

results of numerical simulations with the use of a three-level laser model display good agreement

with experimental results. The mechanism for the rogue wave formation lies in the interplay of

stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a

diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude

pulses perceived as rogue waves. The probability of these events depends on the noise filtered

frequency and grows up when the noise amplitude increases. The probability distribution of spike

amplitudes confirms the rogue wave character of the observed phenomenon. We find the existence

of a particular noise amplitude for which a particular periodic orbit appears more frequently than

for other amplitudes.

1. A.N. Pisarchik, A.V. Kir’yanov, Yu.O. Barmenkov, R. Jaimes-Reátegui, Dynamics of an

erbium-doped fiber laser with pump modulation: theory and experiment, J. Opt. Soc. Am. B

22, 2107-2114 (2005).

ON DYNAMICS AND STATISTICS OF A CONSERVATIVE BOUNCER MODEL: ACCELERATOR AND DECELERATOR MODES

André L. P. Livorati¹, Carl P. Dettmann², and Edson. D. Leonel³

¹ IFUSP - Univ. de São Paulo - USP - SP - Brazil

² Univ. of Bristol - England ³ DEMAC - Univ. Estadual Paulista - UNESP - SP - Brazil


The complete dynamics of a conservative Bouncer model is studied. The time evolution of the system is given by a two dimensional nonlinear mapping in the variables velocity of the particle and phase of the moving boundary. Fixed points were found and characterized. A transition in the fixed points happens when the parameter that controls the ratio of accelerations between the particle and the moving bounary, called $\epsilon$ is bigger than the unity. In this transition, we were able to found accelerator modes which leads the particle to experience the phenomenum of Fermi acceleration with a time proportional, instead of $\sqrt(t)$. As well, we also found decelerator modes in the anti-symmetric position of the accelerator ones, but they shown to be very unstable. A whole numerical and statistical analyis were made in order to identify, localize and understand the influence of these two modes in the system dynamics concerning Fermi acceleration phenomenun.

EVOLUTION OF RNA VIRUSES WITH FREQUENCY-DEPENDENT

SELECTION.

Roberto Álvarez-Martínez

Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México (UNAM),

D.F. México


RNA viruses show rapid adaptation both in laboratory and natural environments. The enormous diversity generated by the high error rates is generally believed to be at the root of such adaptive potential. Clearly, high mutation rates provide increased variation for responding to strong selective pressures, hence accounting for the rapid emergence of drug-resistant viruses, for instance HIV, hepatitis C, polio and inuenza. During 30 years, quasi-species theory has become a standard conceptual frame to study the RNA viruses evolution. However, one of the key problem with this theory is its lack of frequency-dependent selection. In other words, the fitness of a particular phenotype is set to a constant value independently of the other competing 'players'. This can be solved by using the replicator-mutator equations, which represents a general formulation for the evolutionary dynamics. This work proposes, and solves computationally, a modi_edquasi-species model in order to take this condition into account. This modication allow us to study the Shannon entropy, the existence of an error-catastrophe (a second-order phase transition), and the emergence of cooperation, we interpret the results in terms of this more biologically realistic scheme.

"Diffusive properties of Lorentz gases via persistent

random walks"

Dr. David P. Sanders Departamento de Física, Facultad de Ciencias, Universidad Nacional

Autónoma de México

Thomas Gilbert (1), Huu Chuong Nguyen (1) & *David P. Sanders* (2)

(1) Center for Nonlinear Phenomena and Complex Systems, Université

Libre de Bruxelles, C. P.

231, Campus Plaine, B-1050 Brussels, Belgium

(2) Departamento de Física, Facultad de Ciencias, Universidad Nacional

Autónoma de México,

04510 México DF, Mexico

We calculate [1] exact expressions for diffusion coefficients of persistent random walks on

cubic lattices. In these types of random walks, the direction of a walker at a given step

depends on the memory of its direction of motion in one or two previous steps. These

results are then applied to study billiard models, namely two- and three-dimensional

periodic Lorentz gases, with geometry chosen to exhibit normal diffusion. We calculate

numerically the transition probabilities between cells to compare the persistent random-

walk approximation with simulation results for the diffusion coefficient of the Lorentz

gases.

[1] Diffusive properties of persistent walks on cubic lattices with application to periodic

Lorentz gases. Thomas Gilbert, Huu Chuong Nguyen & David P. Sanders.

Normal modes of 1-D elastic networks

Francisco J. Martínez

IIMAS, UNAM, D.F. México

[email protected]

For a string of arbitrary length, where the interaction between particles

occurs within a fixed radius, the analysis is the relationship between mass

distribution and modes of vibration of this system, aiming at finding

localized vibrational modes in the regions higher bulk density. Using the

theory of normal functions and compared the results with those obtained

numerically.

mailto:[email protected]

POSTER SESSION · O. Vazquez-Candanedo and F. M. Izrailev Instituto de Física, Universidad...

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