Finite-time And Fixed-time Synchronization Analysis Of Several Kinds Of Neural Networks

Recently,synchronization and control of neural networks have become one of the important research hotspots of scholars.It can be applied to signal and image processing,associative memory,optimization problems and so on when ensuring that the dynamic behavior of the system reaches the ideal state.Considering the requirements of practical problems and hoping that the synchronization can be completed as fast as possible,the concepts of finite-time synchronization and fixed-time synchronization are introduced.However,in the implementation of neural networks,time delay is universal,and the neural networks will also be affected by various external interferences and influences,which will have a certain impact on the systems.Therefore,it is of great significance to study the synchronization of neural networks with time delay or disturbances.This paper focuses on the study of finite-time or fixed-time synchronization of several types of neural networks with time delay or other disturbances.Under the theoretical support of finite-time synchronization and fixed-time synchronization,some sufficient criteria for the neural networks to realize finite-time synchronization or fixed-time synchronization under the controller are obtained by combining Lyapunov functional method,iterative method,mathematical inequality and some analytical techniques.The main contents are summarized as follows:The finite-time synchronization and fixed-time synchronization of memristive neural networks with time delay and external disturbance under the controller are discussed.Through the Lyapunov functional method,using the finite-time synchronization and fixed-time synchronization theories,the finite-time or fixed-time synchronization criteria to ensure the drive-response systems are given,and the estimation formula of the corresponding synchronization time is obtained.The fixed-time synchronization problem of impulsive neural network is considered.By designing state feedback control,different criteria for realizing fixed-time synchronization are established,and the fixed synchronization time estimation is given.The synchronization problem of the memristive neural network with impulsive is studied.By constructing a suitable Lyapunov function and using the theory of impulsive differential system combined with mathematical inequality and iterative techniques,the finite-time synchronization or fixed-time synchronization conditions and synchronization time calculation of the drive-response systems formulas are derived.