Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory

Abstract

In this paper, a novel kind of stochastic delayed complex networks with multi-weights (SDCNMW) is considered. We first split SDCNMW into multiple stochastic complex networks with single weight. This paper is mainly concerned with the issues of exponential stability for SDCNMW. A global Lyapunov functional is constructed by a graph-theoretical approach based on Kirchhoff’s matrix tree theorem. Razumikhin-type theorem is presented by stochastic stability theory and Razumikhin technique. An easy-verified coefficients-type theorem is also given. Finally, theoretical results are illustrated by stochastic oscillators network successfully.