Stochastic synchronization for time-varying complex dynamical networks

doi:10.1088/1674-1056/21/2/020501

Abstract This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.

Keywords: stochastic dynamical networks synchronization time-varying coupling strength adaptive control

Received: 18 April 2011
Revised: 15 September 2011
Accepted manuscript online:

PACS:	05.10.Gg	(Stochastic analysis methods)
	05.45.Xt	(Synchronization; coupled oscillators)
	02.30.Yy	(Control theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60974139) and the Fundamental Research Funds for the Central Universities (Grant No. 72103676).

Corresponding Authors: Guo Xiao-Yong,xyguomath@126.com
E-mail: xyguomath@126.com

Cite this article:

Guo Xiao-Yong(郭晓永) and Li Jun-Min(李俊民) Stochastic synchronization for time-varying complex dynamical networks 2012 Chin. Phys. B 21 020501

[1]	Strogatz S H 2001 Nature 410 268
[2]	Watts D J and Strogatz S H 1998 Nature 393 440
[3]	Wang X F and Chen G 2003 IEEE Circuits Syst. Mag. 3 6
[4]	Park K, Lai Y C, Gupte S and Kim J W 2006 Chaos 16 015105
[5]	Yu W, Chen G and L? J 2009 Automatica 45 429
[6]	Wang Y, Wang Z and Liang J 2009 J. Phys. A: Math. Theor. 42 135101
[7]	Cao J, Yu W and Qu Y 2006 Phys. Lett. A 356 414
[8]	Lu W and Chen T 2004 IEEE Trans. Circuits Syst. I 51 2491
[9]	Cao J, Li P and Wang W 2006 Phys. Lett. A 353 318
[10]	L? J, Yu X and Chen G 2004 Physica A 334 281
[11]	Zhang H G, Gong D W and Wang Z S 2011 Chin. Phys. B 20 040512
[12]	Li Z, Jiao L and Lee J 2008 Physica A 387 1369
[13]	Yu W and Cao J 2007 Physica A 373 252
[14]	Yu W and Cao J 2007 Neural Proc. Lett. 26 101
[15]	Huang X and Cao J 2006 Nonlinearity 19 2797
[16]	Cao J and Lu J 2006 Chaos 16 013133
[17]	Yu W and Cao J 2007 Physica A 375 467
[18]	Huang D 2005 Phys. Rev. E 71 037203
[19]	Cao J, Wang Z and Sun Y 2007 Physica A 385 718
[20]	Wang Y, Wang Z and Liang J 2008 Phys. Lett. A 372 6066
[21]	Liang J, Wang Z and Liu X 2009 IEEE Trans. Neural Netw. 20 781
[22]	Duan D H, Xu W, Su J and Zhou B C 2011 Chin. Phys. B 20 030501
[23]	Lin W and He W 2005 Chaos 15 023705
[24]	Sun Y and Cao J 2007 Phys. Lett. A 364 277
[25]	Yang X and Cao J 2009 Phys. Lett. A 373 3259
[26]	Yu W, Chen G and Cao J 2011 Asian Journal of Control 13 1
[27]	Yang X and Cao J 2010 Applied Mathematical Modelling 34 3631
[28]	Wang Z, Wang Y and Liu Y 2010 IEEE Trans. Neural Netw. 21 11
[29]	Tang Y, Wong W K, Fang J A and Miao Q Y 2011 Chin. Phys. B 20 040513
[30]	Kolmanovskii V B and Myskis A D 1999 Introduction to the Theory and Applications of Functional Differential Equations (Dordrecht: Kluwer Academic Publishers)
[31]	Mao X 1997 Stochastic Differential Equations and Applications (Chichester: Horwood Pubishing)

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