Passivity And Synchronization Of Coupled Reaction Diffusion Cohen-Grossberg Neural Network

Cohen-Grossberg neural network was presented in 1983,since then,it has provoked considerable attention of numerous researchers.On the one hand,Cohen-Grossberg neural networks can generalize some existing well-known neural network models,such as Hopfield neural networks,cellular neural networks,recurrent neural networks.On the other hand,Cohen-Grossberg neural network has developed many applications in lots of different areas,e.g.,associative memory,pattern recognition,signal and image processing,optimization etc..Recently,there are supplies of research results on dynamical behaviors of Cohen-Grossberg neural networks.However,most researchers did not consider diffusion phenomena.Since the neural network is realized by the electronic circuit,when the electron moves in the uneven electromagnetic field,the diffusion phenomena cannot be avoided.Therefore,it is of great significance to study Cohen-Grossberg neural networks with reaction-diffusion terms.In this paper,we propose four types of coupled reaction-diffusion Cohen-Grossberg neural networks models and analyze synchronization and passivity of the introduced network models.In this article,we successively put forward several coupled reaction-diffusion Cohen-Grossberg neural networks with constant coupling,spatial diffusion coupling,time-varying time-delayed state coupling,switching topology.And by using Lyapunov stability theory,a variety of inequality techniques,graph theory,we study the passivity and synchronization of these coupled reaction-diffusion Cohen-Grossberg neural networks.First,through constructing appropriate Lyapunov functional and utilizing inequality techniques,output-strict passivity,input-strict passivity,passivity and synchronization criteria for coupled reaction-diffusion Cohen-Grossberg neural networks with constant coupling and spatial diffusion coupling are established.Second,considering the finite velocity of signal transmission and channel blockage,the problems of passivity and synchronization for coupled reaction-diffusion Cohen-Grossberg neural networks with time-varying time-delayed state coupling are studied.Third,when node connections fail or new connections appear in the network,the jumping parameters and environment change,the topology of the network may change.Therefore,we also consider the passivity and synchronization of coupled reaction-diffusion Cohen-Grossberg neural networks with switching topology and obtain some sufficient conditions.Finally,several numerical examples are given to prove the validity of the theoretical results.