Dynamical Behavior Of Static Neural Network With Time-varying Delays

Artificial neural network is a very active research area in these years, it is applied in pattern recognition,automatic-control systems,optimization,image processing,signal processing,associative memories and so on . In practical applications, people carry out the functions of the ANN by using electronic. Time delays are inevitably encountered in neural networks because of the artificial factors,the finite switching speed of amplifiers and technical level, and so on. Time delays not only reduce the velocity of transmission, but also cause instability and poor performance of neural networks. So it is important to research dynamical behavior of neural network with time delays.Basing on the different basic variables, the mathematical model of neural networks can be divided into two types—local field neural networks model and static neural networks model. Static neural networks model research outer state of the neuron and it is applied in several recurrent neural networks, for instance Recurrent back-propagation networks,Cellular neural networks,Brain-state-in-a-box type networks, and so on. Most researchers about neural networks focused on the local field models, few paid attention to the static models.In the results of dynamical behavior of static neural network with time delays, most are about constant time delays, few about time-varying delays. In this paper, dynamical behavior of static neural network with time-varying delays will be investigated.This paper is organized as follow. Chapter 1 introduces the general knowledge and presents several important definitions and theorems. In chapter 2, some sufficient criteria of the invariant set and periodic attractor are derived. Particularly, we have provided an estimate on existence range of periodic attractor by using the properties of nonnegative matrices and differential inequality technique. In chapter 3, some sufficient criteria of the existence, uniqueness and exponential stability of the almost periodic solution are derived by using the fixed point theorem of Banach space, nonnegative matrices theory and differential in equality technique. In chapter 4, some sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solution for such delayed neural networks by using the topological degree theory, Young inequality and nonnegative matrices theory.