Globaldynamical Behaviors Of Static Neural Network Models With Time Delays

Artificial neural network is a very active research area in recent years.Recurrent neural net works,as an important type of neural networks can be applied in pattern recognition, ,optimization,image processing,automatic-control systems,signal processing and so on. time-delays are inevitable due to 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 network models and static neural network models.Most current reseaches about recurrent neural networks focused on the local field models.However, static models are widely representive. Many useful neural networks are modeled as static models .So it is important to investigate the static models.In this paper, the author generalizes the static models and investigates their global dynamical behaviors.This paper is organized as follows. Chapter 1 introduces the general knowledge of neural net works at first. Then is the relative knowledge about recurrent neural networks and some questions about this paper.Based on topological degree theory and the linear matrix inequality(LMI) approach , In chapter 2 , a new criterion of global exponential stability for static neural networks is derived,and an example is exploited to show the usefulness of the derived LMI-based stability conditions.In chapter 3,the author investigates the global Exponential robust stability of static neural network models with S-type distributed delays on a finite interval, We present a theorem and a series of corollarys by using Lyapunov functional and Exponential stability theorems.Chapter 4 introduces the application of Matlab in neural networks.The author established a new study arithmetic about MRI networks,and this arithmetic can guareteen if the mode of samples is partible,then we can get the neural networks'weight matrix by the method we have established and it can guareteen the sample is partible.And at last,we use Matlab tools validated the example of chapter 2 is correct.In chapter 5,some possible works can be done are listed.The results in this paper generalize relative papers and are very general;the introduced methods are very practical.So this paper is significant in both theory and practice.