A graph-theoretic approach to exponential stability of stochastic complex networks with time-varying delays

This paper considers a general class of stochastic complex networks with time-varying delays (SCNTVDs). A systematic method of constructing a global Lyapunov function for the complex network is provided by combining graph theory and Lyapunov method. Consequently, some novel and simple sufficient conditions of exponential stability for the SCNTVDs are given. These conditions are presented in terms of the topological structure of networks. In addition, to illustrate the effectiveness and applicability of the proposed theory, a practical model in physics is studied and the numerical simulation is also given.