Razumikhin method to global exponential stability for coupled neutral stochastic delayed systems on networks

Abstract

Global exponential stability for coupled neutral stochastic delayed systems on networks (CNSDSNs) is investigated in this paper. By means of combining the Razumikhin method with graph theory, some sufficient conditions that can be verified easily are derived to ensure the global exponential stability for CNSDSNs. Finally, a specific model of CNSDSNs is discussed, and numerical test manifests the effectiveness of the theoretical results.Then, the trivial solution of system (2.2) is almost surely exponentially stable. Remark 3By applying the Chebushev inequality and Borel-Cantelli lemma, Theorem 3 can be proved. The method is very standard in stochastic analysis [39]. Here, we omit it. From Theorem 3, we can see easily that exponential stability in pth moment implies almost surely exponential stability under some conditions as Mao stated in [39].

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“…it will imply stability of the coupled system. For results on stability of coupled systems on networks, both deterministic and stochastic we refer to [4][5][6][7][8][9][10].…”

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