Intermittent synchronization of reaction–diffusion neural networks with mixed delays via Razumikhin technique

Abstract

This paper revisits the exponential synchronization problem of two identical reaction–diffusion neural networks with Dirichlet boundary conditions and mixed delays via periodically intermittent control. The focus is on developing a new Lyapunov–Razumikhin method such that the overdesign that stems from the existing Lyapunov functional method can be reduced. The novelty of the proposed Lyapunov–Razumikhin method is the ability to provide better estimates on the state variables of the synchronization error system and impose no restriction on delay derivatives. By exploring the reaction–diffusion effect using the extended Wirtinger’s inequality, an improved result on intermittent synchronization is derived. The problem of designing optimal intermittent synchronization controllers is addressed, and an easily computable method to determine the controller gain with minimal norm is presented. Finally, two illustrative examples are presented to show the validity of the obtained results and the superiority over the existing ones.