The Pinning State Of The Coupled Reaction-diffusion Neural Network Is Synchronized With The Spatial Diffusion Feedback

Recently,some researchers have paid their attention to investigating the dynamical behaviors of coupled reaction-diffusion neural networks,especially synchronization.However,most of pinning controllers in the published results of pinning synchronization for coupled reaction-diffusion neural networks were state controllers.There is little research reported on how to let the networks realize synchronization with the help of the spatial diffusion controller.Furthermore,the controllers in these published papers are also linear.To the best of our knowledge,the nonlinear spatial diffusion controller has not yet been studied.Thus,the authors focus on the pinning synchronization for coupled reaction-diffusion neural networks by using linear controller and nonlinear spatial diffusion controller,respectively in this paper.On the other hand,because of the environmental noises and model errors,the exact values of coupled reaction-diffusion neural networks parameters usually may not be obtained.Hence,it is necessary to take the parametric uncertainties into account when we analyze the dynamical behaviors of coupled reaction-diffusion neural networks.However,there are few works on coupled reaction-diffusion neural networks with parametric uncertainties.Therefore,we also paid attention to parametric uncertainties which are changed in some given precisions when studying coupled reaction-diffusion neural networks.In this paper,we study the pinning synchronization for coupled reaction-diffusion neural networks by utilizing some inequality techniques,stability theory,graph theory and pinning control method.Firstly,with the help of pinning state controller and stability theory,some criteria of pinning synchronization for coupled reaction-diffusion neural networks with multiple time-delays are obtained.Secondly,by using the designed nonlinear pinning spatial diffusion controllers and Lyapunov function,some sufficient conditions are derived to make sure the coupled reaction-diffusion neural networks with and without parametric uncertainties can achieve synchronization.Finally,the correctness and effectiveness of the obtained results are confirmed by numerical simulation in some illustrated examples.