Razumikhin-type theorems on exponential stability of stochastic functional differential equations on networks

In this paper, stability problem of stochastic functional differential equations on networks (SFDENs) is investigated. Based on the graph theory and Razumikhin technique, some conditions are captured to guarantee that SFDEN is p-th moment and almost sure exponentially stable. Furthermore, the criterion ensuring the exponential stability for stochastic coupled systems on networks with time-varying delay is established, by applying Razumikhin-type theorem. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.