Asymptotic Behavior Of Infinite Dimensional Dynamical Systems And Applications In Neural Networks

The main aim of this paper is to deal with the asymptotic behavior of infinite dimensional dynamical systems.In chapter 2, several new sufficient conditions for the existence of the invariant sets and attracting sets of a class of partial differential equations with time delays are obtained by using the integral formula of the solution of the Cauchy problem and some methods of modern analysis. The exponential asymptotic stability of Cauchy problem is studied by means of the properties of M-matrix.In chapter 3, sufficient conditions for the boundness, asymptotic properties and exponential decay are derived for solutions of linear systems of integral inequalities with infinite delay. Then nonlinear neutral integro-differential equations with infinite delay are reduced to delay integral inequalities by the variation of parameter formula and some criteria are given for asymptotic stability, uniform asymptotic stability, and exponential asymptotic stability of neutral integro-differential equations.In chapter 4, by using semigroup theory and the inequality techniques, some methods for the existence of the invariant sets and attracting sets and asymptotic stability of functional differential equations in Banach spaces are developed. The methods yield conditions for determining the invariant sets, attracting sets and basin of attraction.Chapter 5 The exponential stability in mean square of stochastic Cohen-Grossberg neural network with time-varying delays is discussed by means of Itoformula, delays differential inequality and the characteristics of stochastic delay neural networks.