Transition to Burst Synchronization on Complex Neuron Networks Zhonghuai Hou( 侯中怀 ) 2007.9 Nanjing Department of Chemical Physics Hefei National Lab of.

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Presentation transcript:

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

Our research interest  Statistical problems in mesoscopic chemical systems  Nonlinear Dynamics on complex networks Complexity + Nonlinearity

A Neuron

Diversity: Morphology + Physiology  Oscillation  Spiking  Bursting  Chaos

Neuron Network  Human Brain: and 10 4 Complex Network Small-World Scale-Free  Big Challenge : Dynamics + Functioning

An interesting phenomenon...  Central Pattern Generator Small microcircuits Rhythmic motor commands  Striking feature Individual: irregular,chaotic bursts Ensemble: regular, rhythmic bursting Mechanism ?

Related study  Chaos Regularization N.F.Rulkov, PRL 86,183(2001)

Related study  Ordering Chaos by Random Shortcuts F. Qi, Z.Hou, H. Xin, PRL 91, (2003)

Related Study M. Wang, Z.Hou, H.Xin. ChemPhysChem 7 ， 579( 2006)  Ordering Bursting Chaos Hindmarsh-Rose (HR) model system

Synchronization of Bursting System  Beyond complete synchronization Spike Syn... Burst Syn...

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  Coupled HR system SW Network: N neurons M added links Parameters: Chaotic

Transition to BS

Phase Trajectories Spike Adding Bursting Bifur...

Phase Transitions

Bursting Mechanism Fast sub-system: Slow Parameter: Fold-Homoclinic(FHC) Fold-Hopf(FH) Homoclinic Shrinking

Local Mean Field Fluctuate Close to 0 Depend weakly on i

Perturbed HR system

Cluster separation Valid + Robust

Remarks Easy Hard Easier 5 SPB 6 SPB FH (Homogeneous)

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

Thank you !