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.


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


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