Synchronization Control Of Memristive Neural Networks With Reaction-diffusion Terms

This paper mainly investigates the synchronization problem of two and multiple memristive neural networks with reaction-diffusion terms.Usually,each node of a system has its own change process,and they can not synchronize themselves.In order to meet the practical needs,we must take some measures to make them interrelated,interactional and eventually being consistent.This article is divided into five chapters,the specific contents are as follows.In Chapter 1,we first review the development history of neural networks,and bring forward the research object of this paper,i.e.the memristive neural networks with reaction-diffusion terms,in combination with the theoretical and practical needs of scientific experiments.Then,by analyzing and summarizing the existing research results,the motivation,method and significance of this study are revealed.Finally,the main contents of this paper are briefly introduced.In Chapter 2,we analyse the finite/fixed-time synchronization of the drive-response system.Firstly,the drive-response system model of memristive neural networks with reaction-diffusion terms is briefly introduced.Then,combining Lyapunov function method,Divergence theorem and inequality techniques,by designing appropriate state feedback controllers,the sufficient conditions for ensuring synchronization of drive-response system are derived.Finally,considering that the synchronization time of fixed-time synchronization is independent of the initial states of the network nodes,one numerical simulation example of fixed-time synchronization of the drive-response system under four different initial values is given.In Chapter 3,we discuss the exponential synchronization of multiple coupled memristive neural networks with reaction-diffusion terms.Firstly,the model of mul-tiple nonlinear coupled networks is briefly introduced.Then,by introducing a special kind of M matrix,the synchronization problem of multiple networks is transformed into the stability problem of synchronization manifold.Secondly,the sufficient cri-teria for ensuring exponential synchronization of the coupled systems are deduced in combination with Lyapunov function method,Divergence theorem and inequality tech-niques.In addition,an matrix inequality criterion which can be solved by MATLAB linear matrix inequality toolbox is also given.Finally,in order to verify the validity of the theoretical results,numerical simulation examples of synchronization of multiple networks under undirected and directed coupled topologies are given respectively.Chapter 4 is discussed on the basis of Chapter 3.When the conditions in Chapter 3 cannot be satisfied,we consider controlling the system in Chapter 3.From the econom-ic point of view,in order to reduce the control cost,we design two distributed pinning controllers,namely,distributed state feedback pinning controller and distributed pin-ning impulsive controller.The sufficient conditions for synchronization of the whole system under these two controllers are discussed.Finally,the main contents of this paper are summarized.By analyzing the advan-tages and disadvantages of this paper,the future research directions are determined.