Stability And Bifurcation Analysis On A Class Of Discrete Systems Of Neural Networks With Delays

Since simplified neural network model was introduced in 1982 by American bio-physicist Hopfield, this model has received increasing interest. More and more people become interested in the study of dynamical behaviors of neural networks. People have been paied more atentation to the exploitation and implementation of the neural network model, and applied it in economics, medicine, pattern recognition, signal processing, automatic control, computer and other aspects. In the past, the main research object was systems without delay. However, neural network model with delay was proposed for the time lag in the process of information transmission. Therefore, the reasearch about neural network model with delay is of great significance both in theory and applications.This paper mainly studies the stability and bifurcation of neural network model with delay, which includes the following two aspects, first, the stability and bifurcation analysis of second-order discrete neural network model with time-delay; second,the stability and bifurcation analysis of the first-order discrete neural network model with time-delay. The paper consists of four chapters.In chapter 1, the establishment and development of neural network model is introduced, at the same time, research status of neural networks model are addressed and some required prior knowledge for this paper are given.In chapter 2, we analyze the characteristic roots of the linear approximation equation by using the stability and bifurcation theory of difference equations, specially focus on the stability and bifurcation type of first-order discrete neural network model with time delay, the sufficient conditions guaranteeing the existence of bifurcation are obtained.In chapter 3, the existing conditions of the stability and bifurcation of two neurous delay discrete neural networks model with multi-delay are considered and Flip,Fold,Neimark-Sacker bifurcation are discussed. By using the normative theorem and the center manifold theoremand, we discuss the direction of Neimark-Sacker bifurcation.In Chapter 4, we summarized the main results of this paper.