Synchronization and control for directly coupled reaction-diffusion neural networks with multiple weights and hybrid coupling

Abstract

This article addresses the synchronization and pinning control problems of directly coupled reaction-diffusion neural networks (RDNNs). The model in this article has the following advantages: 1. the network can be directly coupled; 2. there are multiple coupling matrices to represent different communication channels; 3. the spatial information of RDNNs is also utilized for synchronization along with state information, which is called the hybrid coupling. Since different coupling matrices have different normalized left eigenvectors (NLEVec) corresponding to their zero eigenvalue, the design of Lyapunov functions, which heavily depends on NLEVec, will be prevented. In virtue of the weighted combination of NLEVec for multiple coupling matrices, we demonstrate that if the Chebyshev distance among these NLEVec is less than an allowable bound, then several synchronization and pinning control criteria with sufficiently large coupling strengths can be derived. In addition, the issue of adaptive coupling strengths is also addressed. Some numerical examples are finally simulated to illustrate the effectiveness of acquired results.