Synchronization for Multilink Stochastic Complex Networks via Impulsive Control in Infinite Dimensions

This article studies the synchronization of multilink stochastic complex networks via impulsive control in the sense of infinite dimension. Considering that the existence and uniqueness of solutions are the premises for studying the synchronization of infinite-dimensional stochastic systems, we have proven the existence and uniqueness of mild solutions by combining the mild Itô’s formula, graph theory, and the contraction mapping principle. The restriction on the domain of mild solution is removed, which also makes the contraction coefficient less conservative due to the use of mild Itô’s formula. Then, the criteria for achieving exponential synchronization of infinite-dimensional stochastic systems are obtained with the assistance of graph theory and the Lyapunov method. These criteria are related to a network topology and an average impulsive interval. Finally, the theoretical results are applied to a class of multilink bidirectional associative memory neural networks with reaction–diffusion, and several numerical simulations are given.