Exponential input-to-state stability of stochastic delay reaction–diffusion neural networks

Abstract

This paper considers the mean square exponential input-to-state stability (EISS) for stochastic delay reaction–diffusion neural networks (SDRDNNS). SDRDNNS with distributed input and boundary input are investigated. In addition, constant delay and time-varying delay are considered. With the help of Lyapunov–Krasovskii functional method, Itô formula and Wirtinger-type inequality, delay-dependent sufficient conditions on mean square EISS of SDRDNNS are presented. These sufficient conditions show the effects of time-delay and diffusion term on mean-square EISS. Moreover, by means of numerical simulation, the effectiveness of our theoretical results is illustrated.