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Transition to Burst Synchronization on Complex Neuron Networks

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

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  1. 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

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

  3. A Neuron

  4. Diversity: Morphology + Physiology • Oscillation • Spiking • Bursting • Chaos

  5. Neuron Network • Human Brain: 1011 and104 Complex Network Small-World Scale-Free • Big Challenge : Dynamics + Functioning

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

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

  8. Related study • Ordering Chaos by Random Shortcuts F. Qi, Z.Hou, H. Xin, PRL 91, 064102 (2003)

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

  10. Synchronization of Bursting System • Beyond complete synchronization Spike Syn... Burst Syn...

  11. 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

  12. The model • Coupled HR system SW Network: N neurons M added links Parameters: Chaotic

  13. Transition to BS

  14. Phase Trajectories Bursting Bifur... Spike Adding

  15. Phase Transitions

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

  17. Local Mean Field • Fluctuate • Close to 0 • Depend weakly on i

  18. Perturbed HR system

  19. Cluster separation Valid + Robust

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

  21. 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

  22. Thank you !

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