Cluster synchronization in a network of non-identical dynamic systems

doi:10.1088/1674-1056/20/6/060503

Abstract Cluster synchronization in a network of non-identical dynamic systems is studied in this paper, using two-cluster synchronization for detailed analysis and discussion. The results show that the common intercluster coupling condition is not always needed for the diffusively coupled network. Several sufficient conditions are obtained by using the Schur unitary triangularization theorem, which extends previous results. Some numerical examples are presented for illustration.

Keywords: complex network cluster synchronization diffusive couplings Schur's theorem

Received: 03 November 2010
Revised: 25 January 2011
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Xt	(Synchronization; coupled oscillators)

Fund: Project supported by the "13115" Program, China (Grant No. 2008ZDKG-37), the National Natural Science Foundation of China (Grant Nos. 61072139, 61072106, 60804021, and 61001202), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. Y10000902036, JY10000902039, JY10000970001, and JY10000902001).

Cite this article:

Wu Jian-She(吴建设), Jiao Li-Cheng(焦李成), and Chen Guan-Rong(陈关荣) Cluster synchronization in a network of non-identical dynamic systems 2011 Chin. Phys. B 20 060503

[1]	Boccaletti S, Kurths J, Osipov G, Valladares D L and Zhou C S 2002 Phys. Rep. 366 1
[2]	Arenas A, Díaz-Guilera A, Kurths J, Moreno Y and Zhou C 2008 Phys. Rep. 469 93
[3]	Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47
[4]	Strogatz S H 2001 Nature 410 268
[5]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[6]	Liu Y Z, Jiang C S, Lin C S and Jiang Y M 2007 Chin. Phys. 16 660
[7]	Haeri M and Emadzadeh A A 2006 Phys Lett. A 356 59
[8]	Pecora L M and Carroll T L 1998 Phys. Rev. Lett. 80 2109
[9]	Pecora L M and Carroll T L 1998 Phys. Rev. Lett. 80 2109
[10]	Wang X 2002 Int. J. Bifurc. Chaos 12 885
[11]	Duan Z and Chen G 2009 IEEE Circuits and Systems II 56 679
[12]	Lü J, Yu X and Chen G 2004 Physica A 334 281
[13]	Belykh V, Belykh I and Hasler M 2004 Physica D 195 159
[14]	Belykh V, Belykh I and Hasler M 2004 Physica D 195 188
[15]	Lü J and Chen G 2005 IEEE Trans. Automatic Control 50 841
[16]	Qi G X, Huang H B, Shen C K, Wang H J and Chen L 2008 Phys. Rev. E 77 056205
[17]	Chen T P, Liu X W and Lu W L 2007 IEEE Trans. Circuits Syst. I 54 1317
[18]	Xiao Y Z, Xu W, Li X C and Tang S F 2008 Chin. Phys. B 17 81
[19]	Belykh I, Lange E D and Hasler M 2005 Phys. Rev. Lett. 94 188101
[20]	Nishikawa T, Motter A, Lai Y C and Hoppensteadt F C 2003 Phys. Rev. Lett. 91 014101
[21]	Huang L, Lai Y C and Gatenby R A 2008 Chaos 18 013101
[22]	Lü L, Chai Y and Luan L 2010 Chin. Phys. B 19 080506
[23]	Wang X and Chen G 2002 IEEE Trans. Circuit Syst. I 49 54
[24]	Lu W and Chen T 2006 Physica D 213 214
[25]	Cao J, Chen G and Li P 2008 IEEE Trans. Systems, Man and Cybernetics Part B: Cybernetics 38 488
[26]	Wu J and Jiao L 2007 Physica A 386 469
[27]	Zhou C, Motter A E and Kurths J 2006 Phys. Rev. Lett. 96 034101
[28]	Sun W, Chen Z, Lü Y B and Chen S H 2010 Appl. Math. Comput. 216 2301
[29]	Huang C, Ho D W C and Lu J 2010 Nonlinear Analysis: Real World Applications 11 1933
[30]	Tönjes R, Masuda N and Kori1 H 2010 Chaos 20 033108
[31]	Wu J and Jiao L 2007 Physica A 386 513
[32]	Duan Z, Chen G and Huang L Phys. Rev. E 76 056103
[33]	Gfeller D and Rios P D L 2008 Phys. Rev. Lett. 100 174104
[34]	Li Z and Chen G 2006 IEEE Trans. Circuit Syst. II 53 28
[35]	Cao J, Li P and Wang W 2006 Phys. Lett. A 353 318
[36]	Wu W and Chen T 2008 IEEE Trans. Neural Network 19 319
[37]	Wu J and Jiao L 2008 IEEE Trans. Circuit Syst. II 55 932
[38]	Belykh V N, Osipov G V, Petrov V S, Suykens J A K and Vandewalle J 2008 Chaos 18 037106
[39]	Kanakov O I, Osipov G V, Chan C K and Kurths J 2007 Chaos 17 015111
[40]	Wu W, Zhou W and Chen T 2009 IEEE Trans. Circuit Syst. I 56 829
[41]	Hu M, Xu Z and Yang Y 2008 Chaos 387 3759
[42]	Li K, Small M and Fu X 2008 J. Phys. A: Math. Theor. 41 505101
[43]	Cao J and Li L 2009 Neural Networks 22 335
[44]	Wang K H, Fu X C and Li K Z 2009 Chaos 19 023106
[45]	Li C, Sun W and Kurths J 2007 Phys. Rev. E 76 046204
[46]	Belykh I, Belykh V, Nevidin K and Hasler M 2003 Chaos 13 165
[47]	Lu W, Liu B and Chen T 2010 Chaos 20 013120
[48]	Wu C W and Chua L O 1995 IEEE Trans. Circuit Syst. I 42 430
[49]	Wang X F and Chen G 2002 Physica A 310 521
[50]	Wu J and Jiao L 2008 Physica D 237 2487
[51]	Zhan X 2007 ICCM 2 1
[52]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[53]	Chen G and Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[54]	Horn R A and Johnson C R 1985 Topics in Matrix Analysis (New York: Cambridge University Press)

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