Chaos synchronization in complex networks

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 55, Issue 5, 2008, Pages 1335-1346

  Chen, Maoyin ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Chaos synchronization; Complex networks; Matrix measure; Nonsynchronizability; Synchronizability

Indexed keywords

CHAOS THEORY; SYNCHRONIZATION; TIME VARYING NETWORKS;

ANALYTICAL CONDITIONS; CHAOS SYNCHRONIZATION; COMPLEX MATRICES; CONSERVATIVE SYNCHRONIZATION; MATRIX MEASURES; NONSYNCHRONIZABILITY; SWITCHING CONFIGURATIONS; SYNCHRONIZABILITY;

COMPLEX NETWORKS;

EID: 45549105236     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.916436     Document Type: Article

References (45)

1. R. Albert and A. L. Barabasi, "Statistical mechanics of complex networks," Rev. Mod. Phys., vol. 74, pp. 47-91, 2002.
2. S. Boccaletti, V. Latora, Y. Moreon, M. Chavez, and D.-U. Hwang, "Complex networks: Structure and dynamics," Phys. Rep., vol. 424, pp. 175-308, 2006.
3. P. Erdos and A. Renyi, "On the evolution of random graphs," Publ. Math. Inst. Hung. Acad. Sci., vol. 5, pp. 17-60, 1960.
4. D. J. Watts and S. H. Strogatz, "Collective dynamics of 'small world' networks," Nature, vol. 393, pp. 440-442, 1998.
5. A.-L. Barabasi and R. Albert, "Emergence of scaling in random networks," Science, vol. 286, pp. 509-512, 1999.
6. L. M. Pecora and T. L. Carroll, "Master stability functions for synchronized coupled systems," Phys. Rev. Lett., vol. 80, p. 2109, 1998.
7. M. Barahona and L. M. Pecora, "Synchronization in small-world systems," Phys. Rev. Lett., vol. 89, p. 054101, 2002.
8. X. F. Wang and G. Chen, "Synchronization in scale-free dynamical networks: Robustness and fragility," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 54-62, Jan. 2002.
9. X. Li and G. Chen, "Synchronization and desynchronization of complex dynamical network: An engineering viewpoint," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 7, pp. 1381-1390, Jul. 2003.
10. J. Lü, X. Yu, G. Chen, and D. Cheng, "Characterizing the synchronizability of small-world dynamical networks," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 4, pp. 787-796, Apr. 2004.
11. G. Rangarajan and M. Ding, "Stability of synchronized chaos in coupled dynamical systems," Phys. Lett. A, vol. 296, pp. 204-209, 2002.
12. J. Lü, X. Yu, and G. Chen, "Chaos synchronization of general complex dynamical networks," Phys. A, vol. 334, pp. 281-302, 2004.
13. A. Stefanski, J.Wojewoda, T. Kapitaniak, and S. Yanchuk, "Simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems," Phys. Rev. E, vol. 70, p. 026217, 2004.
14. J. Lü and G. Chen, "A time-varying complex dynamical network model and its controlled synchronization criteria," IEEE. Trans. Autom. Contr., vol. 50, no. 6, pp. 841-846, Jun. 2005.
15. Z. Li and G. Chen, "Global synchronization and asymptotic stability of complex dynamcial netwroks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 1, pp. 28-33, Jan. 2006.
16. C. W. Wu and L. O. Chua, "Application of Kronecker products to the analysis of systems with uniform linear coupling," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 7, pp. 775-778, Jul. 1995.
17. C. W. Wu, "Perturbation of coupling matrices and its effect on the synchronizablility in arrays of coupled chaotic circuits," Phys. Lett. A, vol. 319, pp. 495-503, 2003.
18. C. W. Wu and L. O. Chua, "Synchronization in an array of linearly coupled dynamical systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 4, pp. 430-447, Apr. 1995.
19. C. W. Wu, "Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion, and observer design," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 12, pp. 1257-1261, Dec. 2001.
20. C. W. Wu, "Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 294-297, Feb. 2003.
21. C. W. Wu, "Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 2, pp. 282-286, Feb. 2005.
22. C. W. Wu, "Synchronizability of networks of chaotic systems coupled via a graph with a prescribed degree sequence," Phys. Lett. A, vol. 346, pp. 281-287, 2005.
23. C. W. Wu, "Synchronization in networks of nonlinear dynamical systems coupled via a directed graph," Nonlinearity, vol. 18, pp. 1057-1064, 2005.
24. C. W. Wu, Synchronization in Coupled Chaotic Circuits and Systems. Singapore: World Scientific, 2002.
25. A. E. Motter, C. S. Zhou, and J. Kurths, "Enchancing complex-network synchronization," Europhys. Lett., vol. 69, p. 334, 2005.
26. J. Fan and X. Wang, "On synchronization in scale-free dynamical networks," Phys. A, vol. 349, pp. 443-451, 2005.
27. M. Chen and D. Zhou, "Synchronization in uncertain complex networks," Chaos, vol. 16, p. 013101, 2006.
28. M. Chen, "Some simple synchronization criteria for complex dynamical networks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 11, pp. 1185-1189, Nov, 2006.
29. Y. Chen, G. Rangarajan, and M. Ding, "General stability analysis of synchronized dynamics in coupled systems," Phys. Rev. E, vol. 67, p. 026209, 2003.
30. J. Jost and M. P. Joy, "Spectral properties and synchronization in coupled map lattices," Phys. Rev. E, vol. 65, p. 016201, 2001.
31. W. Lu and T. Chen, "Synchronization of coupled connected neural networks with delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 12, pp. 2491-2503, Dec. 2004.
32. J. Zhou and T. Chen, "Synchronization in general complex delayed dynamical networks," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 4, pp. 733-744, Apr. 2006.
33. R. Amritkar and C. K. Hu, "Synchronized state of coupled dynamics on time-varying networks," Chaos, vol. 16, p. 015117, 2006.
34. J. D. Skufca and E. Bollt, "Communication and synchronization in disconnected networks with dynamic topology: Moving neighborhood networks," Math. Biosci., vol. 1, pp. 347-359, 2004.
35. D. Stilwell, E. Bollt, and D. Roberson,l, "Sufficient conditions for fast switching synchronization in time-varying network topologies," SIAM J. Dyn. Syst., 2006, to appear.
36. I. V. Belykh, V. N. Belykh, and M. Hasler, "Blinking model and synchronization in small-world networks with a time-varying coupling," Phys. D, vol. 195, pp. 188-206, 2004.
37. I. V. Belykh, V. N. Belykh, and M. Hasler, "Connection graph stability method for synchronized coupled chaotic systems," Phys. D, vol. 195, pp. 159-187, 2004.
38. I. V. Belykh, V. N. Belykh, and M. Hasler, "Synchronization in asymmetrically coupled networks with node balance," Chaos, vol. 16, p. 015102, 2006.
39. G. W.Wei, M. Zhan, and C. H. Lai, "Tailoring wavelets for chaos control," Phys. Rev. Lett., vol. 89, p. 284103, 2002.
40. S. I. Nicykescy, Delay Effects on Stability: A Robust Control Approach. London, U.K.: Springer-Verlag, 2001.
41. R. D. Driver, Ordinary and Delay Defferential Equations. New York: Springer-Verlat, 1977.
42. J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
43. J. L. Willems, Stabilitat Dynamischer Systeme. Munchen Wien, Germany: Verlag, 1973.
44. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge University Press, 1985.
45. G. Leonov, A. Bunin, and N. Koksch, "Attractor localization of the Lorenz system," Zeitsch. fur Angewan. Math. und Mech., vol. 67, no. 12, pp. 649-656, 1987.