Brief paper: Global stability analysis for stochastic coupled systems on networks

Authors:
Wenxue Li;Huan Su;Ke Wang
Affiliations:
Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, PR China;Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, PR China;Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, PR China and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

This paper considers the global stability problem for some stochastic coupled systems on networks (SCSNs). We provide a systematic method for constructing a global Lyapunov function for these SCSNs, by using graph theory and the Lyapunov second method. Consequently, a new global stability principle, which has a close relation to the topology property of the network, is given. As an application to the results, we employ the principle to two well-known coupled systems in physical and ecology, and then some easy-verified sufficient conditions which guarantee the global stability are obtained.