Convergence And Hopf Bifurcation And Existence Of Periodic Solution In Delayed Neural Network Model

Now well-know , delayed Hopfield neural network(DHNN)were first proposed by Hopfield in 1984 [1]. They have been widely studied both in theory and application. They have been succssfully applied imaginal research processing , pattern recong-nition and associative memory . To date most research on DHNN has restricted to the stability of a system . Few papers consider the existence of global Hopf bifur-cation.Hence in this thesis , by using of the center manifold theorem of differential equation and invariant topological theory . We describe some important properties of the dynamic behaviors of general class , one and two delayed Hopfield neural networks model , which includes global asymptotic stability , Hopf bifurcation and existence of global periodic solution . It is composed of four chapters .As the introduction in chapter 1 , the history and development of neural networks are reviewed briefly . The background of the neural networks discussed in this thesis is interpreted and the problems to the resolved , the purpose and innovation of the investigation are denoted .In chapter 2 , a general class of delayed neural networks are investigated . we obtained some results about the global asymptotic stability in delayed neural networks .In chapter 3 , a model of neural network with a delay is investigated . We obtained some results about the stability , the existence of Hopf bifurcation and global Hopf bifurcation in delayed neural networks .In chapter 4 , two neural constituting an activator-inhibitor delayed Hopfield neural network model are investigated . We obtained some results about the stability, Hopf bifurcation and existence of global periodic solution in delayed Hopfield neural network .