Synchronization for Multi-link Stochastic Complex Networks via Impulsive Control in Infinite Dimensions

This article studied the synchronization of multi-link 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 the combination of 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 since the use of the mild Itô's formula. Secondly, 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 network topology and average impulsive interval. Finally, the theoretical results are applied to a class of multi-link BAM neural networks with reaction-diffusion, and several numerical simulations are given.