A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 7, 2012, Pages 2997-3004

  Wang, Shuguo ^a,b   Yao, Hongxing ^a   Zheng, Song ^c   Xie, Yong ^a  

^a JIANGSU UNIVERSITY   (China)

^b HOHAI UNIVERSITY   (China)

^c ZHEJIANG UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Adaptive coupling strength; Cluster synchronization; Nonidentical nodes; Time varying delays

Indexed keywords

FEEDBACK CONTROL; SYNCHRONIZATION; TIME DELAY; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

ADAPTIVE COUPLING STRENGTHS; CLUSTER SYNCHRONIZATION; COMPLEX DYNAMICAL NETWORKS; COUPLING NETWORK; COUPLING TIME; DELAY COUPLING; NON-IDENTICAL NODES; NOVEL CRITERION; SYNCHRONIZATION PROBLEM; TIME-VARYING DELAY;

DYNAMICAL SYSTEMS;

EID: 84856419800     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.10.036     Document Type: Article

References (34)

1. Watts D.J., Strogatz S.H. Collective dynamics of 'small-world'networks. Nature 1998, 393:440-442.
2. Barbaasi A.L., Albert R. Emergence of scaling in random networks. Science 1999, 286:509-512.
3. Strogatz S.H. Exploring complex networks. Nature 2001, 410:268-276.
4. Newman M.E.J. The structure and function of complex networks. SIAM Rev 2003, 45:167-256.
5. DeLellis P., diBernardo M., Garofalo F. Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica 2009, 45:1312.
6. Zheng S., Wang S., Dong G., Bi Q. Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling. Commun Nonlinear Sci Numer Simulat 2012, 17:284-291.
7. Porfiri M., Bernardo M.D. Criteria for global pinning-controllability of complex networks. Automatica 2008, 44:3100-3106.
8. Sorrentino F., Bernardo M.D., Garofalo F., Chen G.R. Controllability of complex networks via pinning. Phys Rev E 2007, 75:046103.
9. Xia W., Cao J. Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 2009, 19:13120-13128.
10. Cai S., Liu Z., Xu F., Shen J. Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit. Phys Lett A 2009, 373:3846-3854.
11. Khadra A., Liu X.Z., Shen X. Impulsively synchronizing chaotic systems with delay and application to secure communication. Automatica 2005, 41:1491-1502.
12. Sun W., Hu T., Chen Z., Chen S., Xiao L. Impulsive synchronization of a general nonlinear coupled complex network. Commun Nonlinear Sci Numer Simulat 2010, 10.1016/j.cnsns.2011.02. 032.
13. Lü J., Chen G. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans AC 2005, 50:841-846.
14. Li X., Wang X.F., Chen G. Pinning a complex dynamical network to its equilibrium. IEEE Trans Circuits Syst I 2004, 51:2074-2087.
15. Chen T., Liu X. Pinning complex networks by a single controller. IEEE Trans Circuits Syst I 2007, 54:1317-1326.
16. Liu Y., Wang Z., Liang J., Liu X. Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans Syst Man Cybernetics-Part B 2008, 38:1314-1325.
17. Sun W., Chen S., Wan G. Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling. Phys Lett A 2008, 372:6340-6346.
18. Zheng S., Dong G., Bi Q. Impulsive synchronization of complex networks with non-delayed and delayed coupling. Phys Lett A 2009, 373:4255-4259.
19. Rabinovich M.I. Origin of coherent structures in a discrete chaotic medium. Phys Rev E 1999, 60:1130-1133.
20. Zanette D.H., Mikhailov A.S. Mutual synchronization in ensembles of globally coupled neural networks. Phys Rev E 1998, 58:872-875.
21. Belykh I.V., Belykh V.N., Nevidin K.V., Hasler M. Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos 2003, 13. 165-13.
22. Belykh V.N., Belykh I.V., Hasler M., Nevidin K.V. Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators. Chaos 2003, 13:755-779.
23. Kaneko K. Relevance of dynamic clustering to biological networks. Physica D 1994, 75:55-73.
24. Rulkov N.F. Images of synchronized chaos: experiments with circuits. Chaos 1996, 6:262.
25. Wu W., Zhou W., Chen T. Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans Circuits Syst I 2009, 56(4):829-839.
26. Wu W., Chen T. Partial synchronization in linearly and symmetrically coupled ordinary differential systems. Physica D 2009, 238:355-364.
27. Belykh V.N., Osipov G.V., Petrov V.S., Suykens J.A.K., Vandewalle J. Cluster synchronization in oscillatory networks. Chaos 2008, 18:037106.
28. Ma Z.J., Liu Z.R., Zhang G. A new method to realize cluster synchronization in connected chaotic networks. Chaos 2006, 16:023103.
29. Lu W.L., Liu B., Chen T. Cluster synchronization in networks of coupled noidentical dynamical system. Chaos 2010, 20:013120.
30. Lu W.L., Liu B., Chen T. Cluster synchronization in networks of distinct groups of maps. Eur Phys J B 2010, 77(2):257-264.
31. Wang K.H., Fu X.C., Li K.Z. Cluster synchronization in community networks with nonidentical nodes. Chaos 2009, 19:023106.
32. Wang JY, Feng JW, Xu C, Zhao Y. Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix, Nonlinear Dyn, doi:10.1007/s11071-011-0093-4. doi:10.1007/s11071-011-0093-4.
33. Wu X.J., Lu H.T. Cluster synchronization in the adaptive complex dynamical networks via a novel approach. Phys Lett A 2011, 375:1559-1565.
34. Hu C., Yu J., Jiang H.J., Teng Z.D. Synchronization of complex community networks with nonidentical nodes and adaptive coupling strength. Phys Lett A 2011, 375:873-879.