1. 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

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

3. A Neuron

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

5. Neuron Network  Human Brain: 10 11 and 10 4 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 M. Wang, Z.Hou, H.Xin. ChemPhysChem 7 ， 579( 2006)  Ordering Bursting Chaos Hindmarsh-Rose (HR) model system

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 Spike Adding Bursting Bifur...

15. Phase Transitions

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

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

18. Perturbed HR system

19. Cluster separation Valid + Robust

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

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 !