Stability And Synchronization For Some Kinds Of Discontinuous Neural Network Systems

In recent years,neural network systems have been widely used in combinatorial optimization,adaptive control,signal processing,associative memory,pattern recognition and other engineering fields.The research of neural network systems has attracted the close attention of scholars at home and abroad.Many experts and scholars have discussed the basic properties of the solutions of neural network systems in many ways,which greatly promoted the development of neural networks.Because of the limitations of analytical tools and methods,people have considered continuous neural network systems for a long time.However,in many practical problems and scientific practices,discontinuous neural network systems exist objectively.For discontinuous neural network systems,classical differential equation theory no longer satisfies theoretical research and application.In this paper,the discontinuous neural network system is transformed into corresponding functional differential inclusions by Filippov regularization method.In the basic framework of Filippov functional differential inclusions,the global convergence and synchronization of solutions in the sense of Filippov are discussed.The main contents of this dissertation can be summarized as follows:In the first chapter,the background,significance and research status of neural network are introduced,and the content,current situation and significance of the subject studied by the author are explained in detail.In Chapter 2,the existence and stability of periodic solutions for a class of neutral neural network systems with time-varying delays and impulses are studied.Firstly,some related hypotheses are proposed,and the existence of periodic solutions is proved by using Mawhin coincidence degree expansion theorem.Then,the global exponential stability criterion of periodic solutions is obtained by constructing appropriate Lyapunov functional.Finally,numerical simulation is given It shows the validity of the theoretical results.The impulsive neutral neural network system discussed in this paper shows the vertical characteristics through difference operator,which is totally different from the expression of references.Therefore,our results are an extension of the existing results.In Chapter 3,we study the global exponential convergence of solutions for a class of hybrid discontinuous higher order cellular neural networks(HCNNs)with time-varying Leakage delays.Firstly,some relevant assumptions are given.Then,using differential inclusion theory and inequality techniques,we obtain the criteria for determining the global exponential convergence of HCNNs with timevarying Leakage delays.In order to illustrate the feasibility of the theoretical results.Finally,some numerical examples and simulations are given.In this paper,the global exponential stability of HCNNs solutions in the existing literature is extended to discontinuous cases.In Chapter 4,the problem of fixed-time robust synchronization for a class of discontinuous fuzzy neutral neural network systems with mixed time delays is studied.Firstly,a drive-response neural network system is established.Then,by using differential inclusion theory and Lyapunov-Krasovskii functional and constructing appropriate state feedback control strategy,the determination of fixed-time robust synchronization for drive-response neural network systems is obtained.In this paper,the effects of discontinuous excitation functions,neutral operators and time-delay terms on the fixed-time synchronization of fuzzy neural networks are discussed for the first time.In Chapter 5,considering the ubiquity and uncertainty of external disturbances,the problem of fixed-time robust synchronization for a class of discontinuous neutral neural network systems with uncertain disturbances and time-varying delays is studied.Firstly,the master-slave neural network system is established.Then,the fixed-time of the master-slave neural network system is obtained by using differential inclusion theory,Lyapunov-Krasovskii functional and inequality techniques.The criterion of synchronization and the estimation of synchronization pause time are given.Finally,numerical examples and simulations are used to verify the correctness and validity of the theoretical results.Chapter 6 summarizes and discusses the contents of the research,and looks forward to the future research directions.