The Decay Synchronization Of Coupled Reaction-diffusion Neural Network Is Synchronized With Decay H?

Recently,the synchronization of coupled neural networks has attracted much attention.Convergence rate is an important but hard to estimate accurately in the study of synchronization of coupled neural networks.Hence,the decay synchronization which can accurately provide the convergence rate of a system's solution has gradually become a research hotspot.At the same time,we also note that the decay synchronization of coupled reaction-diffusion neural networks has not been considered in the available results.Therefore,the decay synchronization of multi-weighted and spatial diffusion coupled reaction-diffusion neural networks is studied in this paper.Then,based on the existing results of decay synchronization and H? synchronization,we firstly proposed the definition of decay H? synchronization,and the decay H? synchronization of the considered model is studied.Furthermore,we also consider the coupling delays caused by the different speed of information transmission between neurons,as well as the model with parametric uncertainties caused by equipment limitation and environmental noise in the modeling process.i.e.,we also study the decay synchronization and decay H? synchronization networks model with coupling delays and parametric uncertainties.The main work of this paper lies in the following aspects.First,based on the definition of decay synchronization and H? synchronization,the definition of decay H? synchronization is proposed for the first time.Second,by designing the nonlinear state feedback controller,using the correlation inequality technology and selecting the appropriate Lyapunov functional,we obtain the decay synchronization and decay H?synchronization criteria of the multi-weighted coupled reaction-diffusion neural networks and the multi-weight coupled delayed reaction-diffusion neural networks,respectively.In addition,in order to make the model closer to reality,sufficient conditions are also obtained to ensure the spatial diffusion coupled delayed reaction-diffusion neural network is decay(robust decay)synchronized and decay H?(robust decay H?)synchronized.Finally,some numerical simulation examples are given to prove the correctness and validity of the obtained results.