The Bifurcation Of Several Kinds Of Neural Network With Delays

Artificial neural network is a system that modified the mechanism of deposing message of biological neural network base on actual need. It is a modified system designed by men. the mistakes of synapse contact weight, input, threshold of neuron and delay exist in design. Those mistakes have a effect on the dynamics of a family of dynamical systems. So it is meaningful to study the bifurcation of neural network.This thesis of Master is composed of three chapters.Chapter 1 introduces the background of the problem-researching and the significanceof the research in this field.In chapter 2, we mainly study a three-unit neural network model with time DelaysWe choose b as the bifurcation parameter. The sufficient conditions of the stabilityand the bifurcations at the equilibrium are obtained by analyzing the distribution of the characteristic roots. Furthermore, an explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutionsare derived by using the normal form and the center manifold theory. At last, several numerical simulations to support our theoretically analytical conclusions are carried out using Matlab soft.In chapter 3, we mainly study the existence, direction and stability of the hopf bifurcation of a simplified bidirectional associative memory neural network with delays We chooseÏ„=Ï„₁ +Ï„₂ as the bifurcation parameter. We study the existence, direction and stability of the Hopf bifurcation and the stability of the bifurcating periodic solutions by using the normal form and the center manifold theory. We carry out numerical simulations to support our conclusions.