The Stability Study Of Several Kinds Of Delay Network Of Neurons

Recently,some of the reasons why Hopfield neural works have received a great deal of attention of mathmaticals are because of it can be used in applications to signal and image processing .It is well known that for neural networks with delays, it is rather difficult to analyze their stability properties due to introduction of delays. There are usually two ways to do this. One is to linearize the system near equilibrium, conditions obtained in this way concern the local stability around an equilibrium. Another way is to construct a suitable Liapunov function for system and then to derive sufficient conditions ensuring stability, this usually involves global stability.This dissertation mainly studies the stability of three classes of delayed neural networks.A series of results are obtained , which of them improve or extend the related results in the literatures.This paper consider the stability property of a class of delayed difference equations, we obtain some different conditions ensuring the existence of the equilibrium by means of Brouwer's fixed theorem,and we obtain some conditions ensuring the global exponential stability of the equilibrium by means of the Liapunov functional method.In the study of a class of Hopfield neural network with continuous delays, we obtain some conditions ensuring the existence, uniqueness and the global exponential stability of the periodic solutions by means of degree theorem and Liapunov functional method.Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Our results expand the related results in the literatures. We also give two specific examples to illustrate the obtained results. In this paper ,we also focuse on the bi-directional associative memory network model with distributed delays , by Brouwer's fixed theorem, and by means of the Liapunov functional method, we obtain some different conditions ensuring the existence .uniqueness, and global exponential stability of the equilibrium.