Existence and synchronization of coupled stochastic infinite-dimensional systems via aperiodically intermittent control

This paper analyzes a class of stochastic coupled systems with time-varying delays in infinite dimensions. The existence and uniqueness as a prerequisite to ensure synchronization of the solution is analyzed, based on the idea of the contraction mapping principle, graph theory, and mild Itô's formula. Next, the p-th moment exponential synchronization (PMES) of infinite-dimensional systems is realised using the discrete control strategy, namely, aperiodically intermittent control (AIC). By combining graph theory with the Lyapunov method, several criteria for synchronizing infinite-dimensional systems are obtained using the mild Itô's formula. These criteria show the effects of control parameters, topology, and time delays on PMES. Finally, the theoretical results are applied to a class of neural networks with reaction-diffusion, and some numerical simulations are also given.