Effects Of The Time Delay And Small World Connections On The Stability Of Hopfield Neural Network System

This paper mainly studies the effects of the time delay and small world connections on the stability of Hopfield neural network system.One is about the stability analysis of a kind of Hopfield type delay neural network system,and the other is about the stability for a class of delayed ring neural network with two small world connections.It is arranged as follows:In the first chapter,we introduce the historical background,significance of Hopfield neural network system,the domestic and foreign research status and briefly describe the delay neural network system model.In the second chapter,we analyze the stability conditions of a kind of Hopfield type delay neural network by using the eigenvalue method,and discuss the relationship between the values of time delay and the eigenvalues of the system matrix,the stability conditions and the stability region of system.In the third chapter,we study the stability for a class of a delayed ring neural network with two small world connections.The well-posedness,the delay-independent stability problems,the relationship between the small world connection weights and the system stability are discussed.The stability domains for the small world connections are established.Finally,we verify the validity and feasibility of the conclusion by numerical simulation results.In the fourth chapter,we study the stability for a class of a delayed ring neural network with two small world connections by using Lyapunon stability approach.We analyze the equilibrium point of the system,obtain the delay-dependent stability criterion,and the influence of small world connections on system stability region.Finally,the theoretical results are verified by numerical simulation.