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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
Our research interest
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); ...
Effects of internal noise near HB
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);
Effects of internal noise near HB
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
Dynamics of coupled nonlinear oscillators on complex networks
Our research interest
Spatiotemporal evolution
Clustering
Amplitude death
Bifurcation and phase transition
Other than synchroni-
zation
Our research interest
Dynamics of coupled nonlinear oscillators on complex networks
Chaotic oscillator
Relaxation oscillator
Limit-cycle oscillator
Chaotic map
Our research interest
Dynamics of coupled nonlinear oscillators on complex networks
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
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)
Frequency selective response
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 !
Frequency selective response
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
