Global synchronization of stochastic delayed complex networks
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O R I G I N A L PA P E R
Global synchronization of stochastic delayed complex networks Bo Song · Ju H. Park · Zheng-Guang Wu · Ya Zhang
Received: 22 May 2012 / Accepted: 21 September 2012 / Published online: 10 October 2012 © Springer Science+Business Media Dordrecht 2012
Abstract This paper is concerned with the delaydependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the Itô integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important probB. Song · J.H. Park () · Z.-G. Wu Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea e-mail: [email protected]
lem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delaydependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Keywords Complex networks · Stochastic systems · Delay · Synchronization · Delay-dependent criterion
B. Song e-mail: [email protected]
1 Introduction
Z.-G. Wu e-mail: [email protected]
As is known to all, complex dynamical networks (CDNs) widely exist in the real world, including foodwebs, ecosystems, metabolic pathways, the Internet, the world wide web, social networks, and global economic markets [1, 2]. Since the discoveries of the small-world feature [3] and the scale-free feature [4] of complex networks, the analysis and the control of the dynamical behaviors in complex networks have attracted a great deal of attention. As a significant collective behavior, the studies on synchronization phenomena of complex dynamical networks have been extensively investigated in [5–11]. Recently, it has now been well realized that in spreading information
B. Song School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou, Jiangsu 221116, P.R. China Z.-G. Wu National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, Zhejiang 310027, P.R. China Y. Zhang School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221000, P.R. China e-mail: [email protected]
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through complex networks, there always exist time delays caused by the finite speed of information transmission and the limit of bandwidth, which may decrease the quality of the system and even lead to
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