Stability Analysis And Synchronization Control Of Neural Networks With Time Delay

Neural network is an information processing system to simulate the structures and functions of the human brain.It is widely used in associative memory,optimization,signal processing,pattern recognition and secure communication.However,these applications are all based on the fact that the dynamic behaviors and synchronization states of the system are ideal.In addition,time delay is inevitable in the implementation of neural networks,which often leads to bad behaviors.Therefore,it is of theoretical and practical significance to study the dynamic behaviors of delayed neural networks.This paper is devoted to the study of several kinds of neural networks with time delay.Some sufficient criteria for the stability and synchronization of neural networks with time delay are obtained via LMI method,Lyapunov functional method,matrix measure method,generalized Halanay inequality and some analysis techniques.The main works of this paper are summarized as follows:The local exponential stability of a class of neural networks with state-dependent delay is discussed.By pure analysis method and technique of reduction to absurdity,some sufficient criteria for the local exponential stability of the system are obtained.The quantization synchronization of a class of chaotic master-slave neural networks with constant time delay under event-triggered control is studied.Under a given dynamic event-triggered strategy,a feasible controller is designed by using LMI method and generalized Halanay inequality to ensure the realization of quasi-synchronization of chaotic master-slave neural networks.Meanwhile,the estimation of synchronization error bound and the lower bound of sampling interval are given.Multi-mode function synchronization of memristive neural networks with mixed delays and parameters mismatch under event-triggered control is discussed.By Lyapunov functional method,matrix measure method and an improved Halanay inequality,the multi-mode function synchronization of memristive neural networks with state-dependent parameters mismatch and the multi-mode function synchronization of memristive neural networks with structure-dependent parameters mismatch are realized,respectively.The results improve the existing results.In this paper,the dynamic behaviors of several kinds of neural networks with time delay under different conditions are studied,especially the study of neural networks with state-dependent delay,which may interest researchers in engaging the theory and application of the new neural network models having kinematics and dynamics feature.