Relative Research On Memristor-based Neural Network With Discontinuous Activation Function With Mixed Time-varying Delay

In this paper,the dissipativity and synchronization problems of memristor-based neural networks with mixed time-varying delays are studied.Firstly,in the framework of generalized Filippov differential inclusion theory,the global dissipativity properties of Filippov solutions of neural networks are proved by using the method of generalized Halanay inequality and matrix measure.Then,we construct some suitable Lyapunov functions,use some analysis techniques and appropriate inequalities,we design several discontinuous feedback controllers,and realize the synchronization of neural network drive system and response system.Numerical simulation is carried out based on programming,and the validity and correctness of the results are verified by several examples.The paper is divided into five chapters.The first chapter is the introduction part.Firstly,it introduces the formation and development of memristor-based neural network with mixed time-varying delay discontinuous activation function.Secondly,it introduces the characteristics of memristor-basedand the development status of memristor-based neural network.Finally,it introduces the memristor-based neural network with mixed time-varying delay discontinuous activation function.In the second chapter,the dissipativity and exponential synchronization problems of Nonautonomous Hopfield neural networks with mixed time-varying delays and discontinuities are studied.By using the discontinuous state feedback controller,using the inequality scaling technique and some theoretical analysis,we finally prove the global exponential synchronization of the drive system and the response system of the neural network.In the third chapter,we study the dissipativity and finite time synchronization problems of MNNs with mixed time-varying delay and discontinuous activation function.Also,in the framework of extended Filippov differential inclusion theory,we obtain several effective new criteria.The global dissipativity properties of Filippov solution of neural network are proved by using generalized Halanay inequality and matrix measure method.Under the condition of inequality reduction and some analysis techniques,we design a simple Lyapunov function and a nonlinear feedback controller.At last,we obtain some new sufficient conditions to ensure the finite time synchronization of MNNs,thus realizing the finite time synchronization of neural network drive system and responsesystem.In the fourth chapter,we study the fixed-time synchronization of mixed time-varying delay memristor-based fuzzy cellular neural networks(MFCNN)with discontinuous activations.Firstly,by extending the framework of Filippov differential inclusion theory,the timing synchronization of neural network drive system and response system is derived.At the same time,based on a new Lyapunov function and two new nonlinear feedback controllers,some new sufficient conditions are obtained to ensure the timing synchronization of MFCNNs drive-response system.In the fifth chapter,the content of the paper is summarized,and the possible research direction in the future is pointed out.