Spatiotemporal dynamics of coupled nonlinear oscillators on complex networks

Spatiotemporal dynamics of coupled nonlinear oscillators on complex networks

Zhonghuai Hou( 侯中怀 )2006.12 Beijing

Department of Chemical PhysicsHefei National Lab of Physical Science at Microscale

University of Science and Technology of China

Our research interest

Statistical problems in mesoscopic chemical systems

Dynamics of coupled nonlinear oscillators on complex networks

Complexity + Nonlinearity


Statistical problems in mesoscopic chemical systems

Nano-thermodynamics

Nonlinear chemical dynamics

Fluctuation theorems

Effects of fluctuation

Effects of internal noise near HB

System Size Resonance

1.4 1.6 1.8 2.0 2.2 2.4 2.60.4

0.8

1.2

1.6

2.0

2.4

2.8

Con

cent

ratio

n X

1

Control parameter B

V=1E4

Stochastic OscillationA=1, B=1.95

4

1

1: ( ) ( ) ( )j j jj

CLE dX F dt v w dW tV

X X

ChemPhysChem 5, 407(2004); J.Chem.Phys. 119,11508(2003); J.Phys.Chem.A 109, 2745(2005); J.Phys.Chem.B 108,17796(2004); Chem.Phys.Lett. 401,307(2005); ...


System Size Bi-Resonance

ChemPhysChem 5, 1041(2004); 7, 1520(2006); J.Chem.Phys. 122, 134708(2005); J.P

hys.Chem.A 109, 8715(2005);


Two System Size Resonances

N 个耦合的介观化学振荡体系……V V V V

N

Log(V)

ChemPhysChem 5, 1602(2004); Phys.Rev.E 74, 031901(2006)

Optimal number of noisy oscillators of optimal size function the best



Spatiotemporal evolution

Clustering

Amplitude death

Bifurcation and phase transition

Other than synchroni-

zation



Chaotic oscillator

Relaxation oscillator

Limit-cycle oscillator

Chaotic map



Regular(K neighbors)

Scale-Free ...

Global coupled

Small-World(WS/WN) Key

features of

network topology

Today’s Contents

System Phenomenon

Chaotic oscillator

Relaxation oscillator

Limit-cycle oscillator

Chaotic map

Taming chaos

Optimal coherence

Oscillation death

Pattern branching

Driven oscillator Frequency selection

Taming Chaos

Ordering Chaos by Random shortcuts F. Qi, Z.Hou, H.Xin. Phys.Rev.Lett. 91, 064102(2003)

2 sin ' sin ( )n n n n n nm m nm

ml mgl t k

Taming Chaos

Ordering Spatiotemporal Chaos in Complex Neuron Networks M. Wang, Z.Hou*, H.Xin. ChemPhysChem 7， 579( Mar 2006)

3 2

2

0

j j j e i i j

j j j

j j

x y ax bx z I x x

y c dx y

z r s x x z

?

Pattern branching

stable

unstable

3

( )3

( )

i ii i j i

j

ii i i

dx xx y g x x

dt

dyx a D t

dt

Optimal coherence

22T T T 1

1( ) ( )

N

out ii

x t x tN

ChemPhysChem, 6, 1042(2005); Chin.Phys.Lett. 23(10), 2666(2006)

Oscillation death2

( ) ( )j j j j j i ji

z i z r z z d z z

2

1

N

jj

z

ENr

2

1

2

N

jj

z

WN r

K=4,p=0

Oscillation death

Oscillator death on small-world networks Z.Hou, H.Xin, Phys.Rev.E 68,055103R(2003)

Frequency selective response

4, 9i eT T Global Coupled Network

G. Zhao, Z. Hou, H. Xin, Phys.Chem.Chem.Phys. 7,3634(2005)


From regular to global

Single: Fast; Global: Slow

G. Zhao, Z. Hou, H. Xin, Chaos 16, 043107(2006)

Concluding remarks Spatiotemporal chaos observed in a regular network can

be tamed into ordered state via adding an optimal number of random shortcuts

Coupled noisy relaxation oscillators show best coherence in time when an optimal number of random shortcuts are added to a regular network

Network topology show a nontrivial effect on oscillation death, namely, partial death can be eliminated, and global death can be induced

Larger network response more frequently to slow external signal than to the fast internal signal in coupled noisy FHN neuron models

Fast transition from internal signal to external signal response happens within a narrow change of the number of random shortcuts

Thank you !


4, 9i eT T

G. Zhao, Z. Hou, H. Xin, Phys.Chem.Chem.Phys. 7,3634(2005)

Single Isolated Oscillator

0 5000 10000 15000 20000 25000 30000 35000

0.4

0.6

0.8

1.0

lambda1

nLine

Spatiotemporal dynamics of coupled nonlinear oscillators on complex networks

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