| Artificial neural network is a very active research area in these days , it is applied in pattern recognition ,automatic-control system ,optimization, image processing ,signal processing ,associative memories and so on. In practical applications, people carry out the function of the ANNs 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 delay 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 networks with time delay .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 delay ,few about time-varying delay.This paper is organized as follow:Chapter 1 introduces the general knowledge and presents several important definitions and theorems. In chapter 2, a discrete-time Cohen-Grossberg Neural Network with variable delay is studied. Existence of periodic solutions is investigated by using the continuation theorem of coinicdence degree theory. In chapter 3, By using properties M-matrix ,method of Liapunov function and inequality technique, the authors study the existence and global asymptotically stable of a class of static recurrent neural networks with delays, and a new criterion was given. |
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