Dynamics On Two Class Of Neural Networks With Distributed Delays

This paper studies the existence and exponential stability of the equilibriumpoint for two classes of neural network model with continuously distributed de-lays.The first model is subject to delays distributed over bounded intervals, whosedynamical behavior is described by the following form of functional differentialequation:While the second is subject to delays distributed over unbounded intervals, whichcan be described as follows:The paper is organized as follows. In the first chapter, the background andthe necessity for the study of neural networks are presented. Then, some knownresults of neural network models are introduced. And the main work of this paperis also simply introduced. In the second chapter, we shall introduce some founda-tion knowledge needed in the paper such as definitions, lemmas and notations. Inthe third chapter, we consider the dynamical behaviors of the first class of neuralnetwork. By using Cramer rule and Brouwer's fixed point theorem, a new suffcientcondition is derived for the existence of the equilibrium point. Based on the delaydifferential inequality, we obtain effective result for analyzing the stability of cel-lular neural networks with continuously distributed delays. In the fourth chapter,by using contraction mapping principle and the technique of Halanay inequalities,it is proved that there is a globally exponentially stable unique equilibrium statein the second class of neural network.