Stability Of Several Types Of Delay Hopfield Neural Networks

Hopfield neural network has a wide range of applications in pattern recognition,associative memory,parallel operations,and difficult optimization problems.In these applications,the dynamic properties of Hopfield neural network play an important role,so the dynamic behavior of Hopfield neural network is particularly It is the stability problem that has been extensively studied.This thesis mainly discusses the stability of the multi-scale delay Hopfield neural network,the variable delay pulse Hopfield neural network,and the high-order pulse constant delay Hopfield neural network.The first chapter describes the development history of Hopfield neural network,the research history and current research status of the stability of time-delay neural network.The second chapter studies the Hopfield neural network with multiple scale delays,using Barbalat's lemma and the inequality technique of 2ab?a~2+b~2,constructing a suitable Lyapunov functional,and obtaining a global asymptotic stability of the Hopfield neural network Sufficient conditions.The third chapter studies the existence and uniqueness of the equilibrium point of the pulsed Hopfield neural network with variable delays,and constructs two new Lyapunov functionals to obtain the global uniform asymptotic stability and global exponential stability of the pulsed Hopfield neural network with variable delays.condition.In Chapter four,using the methods of iteration and inequality,the sufficient conditions for the existence and uniqueness of periodic solutions of a second-order impulsive Hopfield neural network with constant delay and the uniform stability of the periodic solutions are obtained.