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Global stability analysis for stochastic coupled systems on networks. (English) Zbl 1209.93158

Summary: 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 Lyapunov’s 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.

MSC:

93E15 Stochastic stability in control theory
93D20 Asymptotic stability in control theory
94C15 Applications of graph theory to circuits and networks
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