Stability and Synchronization of Nonautonomous Reaction–Diffusion Neural Networks With General Time-Varying Delays

This article investigates the stability and synchronization of nonautonomous reaction–diffusion neural networks with general time-varying delays. Compared with the existing works concerning reaction–diffusion neural networks, the main innovation of this article is that the network coefficients are time-varying, and the delays are general (which means that fewer constraints are posed on delays; for example, the commonly used conditions of differentiability and boundedness are no longer needed). By Green’s formula and some analytical techniques, some easily checkable criteria on stability and synchronization for the underlying neural networks are established. These obtained results not only improve some existing ones but also contain some novel results that have not yet been reported. The effectiveness and superiorities of the established criteria are verified by three numerical examples.

I. Introduction

As one of the important ways to realize artificial intelligence, the neural network has been widely investigated in the past decades to improve its computing ability and extend its scope of application. The dynamics of neural networks can help to simulate certain functions of the brain, such as associative memory [1], and solve some engineering problems, such as optimization [2]. These advantages have prompted the dynamics of neural networks to become a hot research topic.