Dynamical Behavior Of Two Classes Of Neural Networks With Time 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. local field neural networks model research on inter state of the neuron, Hopfield networks and Cellular neural networks are the typical representatives; 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,Brain-state-in-a-box type networks, and so on.In the research of dynamical behavior of neural networks, Cellular neural network is one of the most popular ANN(Artificial Neural Network),especially for the models with time delays. They are applied broadly on the pattern recognition,signal-image processing,associative memories,automatic-control systems, and this kind of model will be researched in chapter 2. In addition, the stability analysis issue for reaction-diffusion neural networks with time delays has been an attractive subject of research,but the stability analysis problem for static neural networks with reaction-diffusion terms has only received very little research attention, we will discuss the global exponential stability for the following delayed static cellular neural networks with reaction-diffusion terms in chapter 3.This paper is organized as follows. Chapter 1 introduces the general knowledge briefly and presents several important definitions and theorems. In chapter 2, cellular neural networks with time varying delays are considered; some new sufficient conditions are given for global asymptotic stability and exponential stability by using the Lyapunov stability theorem. In chapter 3, Employing topological degree theory and Lyapunov functional methods, we analyze the global exponential stability of a class of reaction-diffusion static cellular neural networks with time-varying delays. Some new criteria related to the existence of unique equilibrium point and its global exponential stability is obtained. In chapter 4, we discuss the boundedness of solutions for a class of second order nonlinear differential equations with time delays, some new criteria about the boundedness are derived.