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Transition to Burst Synchronization on Complex Neuron Networks. Zhonghuai Hou( 侯中怀 ) 2007.9 Nanjing Department of Chemical Physics Hefei National Lab of Physical Science at Microscale University of Science and Technology of China. Our research interest.

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transition to burst synchronization on complex neuron networks

Transition to Burst Synchronization onComplex Neuron Networks

Zhonghuai Hou(侯中怀)

2007.9 Nanjing

Department of Chemical Physics

Hefei National Lab of Physical Science at Microscale

University of Science and Technology of China

our research interest
Our research interest
  • Statistical problems in mesoscopic chemical systems

Complexity + Nonlinearity

  • Nonlinear Dynamics on complex networks
diversity morphology physiology
Diversity: Morphology + Physiology
  • Oscillation
  • Spiking
  • Bursting
  • Chaos
neuron network
Neuron Network
  • Human Brain: 1011 and104

Complex

Network

Small-World

Scale-Free

  • Big Challenge : Dynamics + Functioning
an interesting phenomenon
An interesting phenomenon ...
  • Central Pattern Generator

Small microcircuits

Rhythmic motor commands

  • Striking feature

Individual: irregular,chaotic bursts

Ensemble: regular, rhythmic bursting

Mechanism ?

related study
Related study
  • Chaos Regularization

N.F.Rulkov,

PRL 86,183(2001)

related study1
Related study
  • Ordering Chaos by Random Shortcuts

F. Qi, Z.Hou, H. Xin, PRL 91, 064102 (2003)

related study2
Related Study
  • Ordering Bursting Chaos

Hindmarsh-Rose (HR) model system

  • M. Wang, Z.Hou, H.Xin. ChemPhysChem 7,579( 2006)
synchronization of bursting system
Synchronization of Bursting System
  • Beyond complete synchronization

Spike Syn...

Burst Syn...

the present work
The present work

Fixed Network + increased coupling

  • Transition from chaos to BS
  • Different types of BS-states
  • Spike-adding
  • Bursting bifurcation
  • Dynamic cluster separation
  • Homoclinic orbits shrinking
  • Local mean field analysis
the model
The model
  • Coupled HR system

SW Network:

N neurons

M added links

Parameters:

Chaotic

phase trajectories
Phase Trajectories

Bursting

Bifur...

Spike

Adding

bursting mechanism
Bursting Mechanism

Homoclinic Shrinking

Fast sub-system:

Slow Parameter:

Fold-Homoclinic(FHC)

Fold-Hopf(FH)

local mean field
Local Mean Field
  • Fluctuate
  • Close to 0
  • Depend weakly on i
cluster separation
Cluster separation

Valid + Robust

remarks
Remarks

Easier

5 SPB

(Homogeneous)

6 SPB

Hard

Easy

FH

conclusion
Conclusion
  • Transition to BS is investigated
  • Two distinct types of transition
  • Neuron degree is important
  • Local mean field approximation
  • Large, Homogeneous HR network with many random links in between can show transition from spatiotemporal chaos to

BS-states with FHC- and FH-bursting