Dynamical Behavior of Nonautonomous Stochastic Reaction–Diffusion Neural-Network Models.

This brief investigates nonautonomous stochastic reaction–diffusion neural-network models with S-type distributed delays. First, the existence and uniqueness of mild solution are studied under the Lipschitz condition without the linear growth condition. Due to the existence of a nonautonomous reaction–diffusion term and the infinite dimensional Wiener process, the criteria for the well-posedness of the models are established based on the evolution system theory. Then, the S-type distributed delay, which is an infinite delay, is handled by the truncation method, and sufficient conditions for the global exponential stability are obtained by constructing a simple Lyapunov–Krasovskii functional candidate. Finally, neural-network examples and an illustrative example are given to show the applications of the obtained results. [ABSTRACT FROM AUTHOR]