Hopf Bifurcation Analysis Of Two Kinds Of Neural Network Models With Time Delay Bidirectional Associative Memory

In this paper,the stability of Hopf at the positive equilibrium point,the conditions for the existence of Hopf branches and the directions and periodic solutions of Hopf branches of two kinds of neural network models with time delay are studied.The first chapter mainly introduces the background and significance of delay differential equations and artificial neural networks and the research status at home and abroad.Some definitions and theorems of system stability and Hopf bifurcation theory are introduced in detail.In chapter 2,a class of five-dimensional BMA neural network model with double delay is studied,and the sufficient conditions for the asymptotic stability of the equilibrium point and the conditions for the generation of Hopf branches are obtained.In chapter 3,a class of six-dimensional BMA neural network model with multiple time delays is studied,the sufficient conditions for the asymptotic stability of the equilibrium point and the conditions for the generation of Hopf bifurcation are obtained,and the specific expressions for determining the direction of Hopf bifurcation and the stability and period of the bifurcation periodic solution are given.Finally,the work of this paper is summarized and the future research direction is prospected.