Spatiotemporal dynamics of coupled nonlinear oscillators on complex networks

1. Spatiotemporal dynamics of coupled nonlinear oscillators on complex networks Zhonghuai Hou(侯中怀) 2006.12 Beijing 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 • Dynamics of coupled nonlinear oscillators on complex networks

3. Our research interest Statistical problems in mesoscopic chemical systems Nano-thermodynamics Fluctuation theorems Nonlinear chemical dynamics Effects of fluctuation

4. Effects of internal noise near HB • System Size Resonance 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); ...

5. Effects of internal noise near HB • System Size Bi-Resonance ChemPhysChem 5, 1041(2004); 7, 1520(2006); J.Chem.Phys. 122, 134708(2005);J.Phys.Chem.A 109, 8715(2005);

6. Effects of internal noise near HB N个耦合的介观化学振荡体系 …… V V V V N • Two System Size Resonances Log(V) Optimal number of noisy oscillators of optimal size function the best ChemPhysChem 5, 1602(2004); Phys.Rev.E 74, 031901(2006)

7. Our research interest Spatiotemporal evolution Clustering Amplitude death Bifurcation and phase transition Dynamics of coupled nonlinear oscillators on complex networks Other than synchroni-zation

8. Our research interest Dynamics of coupled nonlinear oscillators on complex networks Chaotic oscillator Chaotic map Relaxation oscillator Limit-cycle oscillator

9. Our research interest Dynamics of coupled nonlinear oscillators on complex networks Regular(K neighbors) Key features of network topology Small-World(WS/WN) Scale-Free ... Global coupled

10. Today’s Contents System Phenomenon Chaotic oscillator Taming chaos Chaotic map Pattern branching Relaxation oscillator Optimal coherence Limit-cycle oscillator Oscillation death Frequency selection Driven oscillator

11. Taming Chaos • Ordering Chaos by Random shortcuts F. Qi, Z.Hou, H.Xin. Phys.Rev.Lett. 91, 064102(2003)

12. Taming Chaos ? • Ordering Spatiotemporal Chaos in Complex Neuron Networks M. Wang, Z.Hou*, H.Xin. ChemPhysChem 7，579( Mar 2006)

13. Pattern branching stable unstable

14. Pattern branching stable unstable

15. Optimal coherence • ChemPhysChem, 6, 1042(2005); Chin.Phys.Lett. 23(10), 2666(2006)

16. Oscillation death K=4,p=0

17. Oscillation death • Oscillator death on small-world networks Z.Hou, H.Xin, Phys.Rev.E 68,055103R(2003)

18. Frequency selective response Global Coupled Network • G. Zhao, Z. Hou, H. Xin, Phys.Chem.Chem.Phys. 7,3634(2005)

19. Frequency selective response Single: Fast; Global: Slow From regular to global • G. Zhao, Z. Hou, H. Xin, Chaos 16, 043107(2006)

20. 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

21. Thank you !

22. Frequency selective response Single Isolated Oscillator • G. Zhao, Z. Hou, H. Xin, Phys.Chem.Chem.Phys. 7,3634(2005)