Dynamical Hehavior Of A Class Of Competivie Neural Networks With Distrbuted Tiem Delys

Competitive neural networks is an important type of unsupervised learning method of neural networks. As a result of the broad spectrum of applications in signal processing, image processing, pattern recognition and control theory and so on, the competitive neural network has been fully developed. Therefore, the study of competitive neural network dynamic features such as stability, invariant set and attractor has become an indispensable prerequisite in the competitive neural network design. From the point of view about biological ,The human memory contains long-term memory (LTM)and short-term memory(STM).So the complex neural network that contains long-term memory and short-term memory have an important attention in theoretical research and engineering application.The dynamical behavior of a class of competitive neural networks with distributed time delays were discussed in this paper.In the first chapter, the general knowledge of neural networks is introduced, and the preliminary knowledge which is used in the thesis is given.In the second chapter, by using the theory of topological degree and Lyapunov functional methods, the global asymptotic stability of a class of competitive neural networks with distributed time delays is discussed. The existence uniqueness and global asymptotic stability of equilibrium point are investigated. The result is illustrated by an example.In the third chapter, by using the theory of nonnegative matrices and differential inequalities technique the invariant and attracting sets of a class of competitive neural networks with distributed time delays is discussed. The sufficient condition of the invariant and attracting sets of this class of competitive neural networks given. The result is illustrated by an example.In the fourth chapter, this paper studies the exponential stability of competitive neural networks with distributed time delays by making use of the homoeomorphism theory, the idea of vector Lyapunov function , M matrix theory and inequality technique. The existence uniqueness and global exponential stability of equilibrium point are investigated. This paper neither uses the traditional Lipschitz function nor outputs the f unction collection to satisfy the Lipschitz condition.The result is illustrated by an example.