Pinning Control For Passivity And Synchronization Of Coupled Memristive Reaction–diffusion Neural Networks

Nanodevice memristors have been widely used in signal processing,logic operation,artificial neural networks and many other fields since they were developed by HP lab in2008.Because the information processing and storage characteristics of memristors arevery similar to the biological synapses,the memristive neural networks have aroused theinterest of the majority of scholars.In recent years,the research on the dynamical be-haviors of memristive neural networks has been abundant.However,only a few of theworks have considered the diffusion phenomena.As is known to all,neural networksare realized by electronic circuits,so the diffusion phenomena are unavoidable when theelectron is transmitted in non-uniform magnetic field.Therefore,a kind of coupled mem-ristive reaction-diffusion neural network model with time-varying delay is proposed inthis dissertation.Specifically,the main research works and results of this dissertation areas follows:First,considering the coupling effect between networks,the diffusion phenomenaand the time delay which cannot be ignored during the implementation of neural networks,the existing models of memristive neural network are improved and a new model calledcoupled memristive reaction–diffusion neural network model is established.Second,based on the above network model,the passivity and synchronization of thenetworks are studied.By making use of the node-based pinning control strategy and con-structing appropriate Lyapunov functionals,several passivity and synchronization criteriaof coupled memristive reaction–diffusion neural networks with time-varying delay are de-rived.Finally,the correctness and effectiveness of the results are verified by MATLABsimulation.Third,another kind of edge-based adaptive pinning controller is designed to furtherstudy the passivity and synchronization of coupled memristive reaction-diffusion neural networks.Some sufficient conditions are obtained to ensure the passivity and synchronization of the networks by taking full advantage of Lyapunov functional,green's formula,Schur complement lemma and other tools.At last,a numerical example is provided to verify the correctness of the theoretical results.The research results of this dissertation supplement and enrich the existing results at home and abroad to a certain extent,which lay the foundation for a better simulation of artificial neural networks and bring new hope for solving more complex application problems in the field of artificial intelligence.