Global Asymptotic Dynamical Behavior Of Recurrent Neural Networks With Time Delays

Due to the broad spectrum of applications in optimization, signal processing, image processing, pattern recognition, associative memories and so on, the artificial neural networks (ANN) have been fully developed.Because the function in information processing is determined by dynamic quality of the artificial neural networks, it is necessary to investigate the dynamic quality such as stability. Especially, in the applications of optimization, neural control, signal processing and pattern recognition, the global asymptotic stability has become the core problem in research in order to avoid local minima.In the realization of electronic neural networks, time delays are likely be present due to the finite switching speed of amplifiers, which will affect the stability and lead to the oscillation and therefore influence the function of the artificial neural networks. So, the dynamic behavior of the three kinds of artificial neural networks models with delays have been investigated in this thesis.The paper is divided into 4 chapters. Chapter 1 introduces the general knowledge, the main works and some preliminaries of this paper.In chapter 2, global robust stability for competitive neural networks with time delays and different time scales has been discussed by employing topological degree theory, homotopy invariance theorem, functional inequality and Liapunov functional method, and the fairly general and convenient criteria of global robust stability have been presented.In chapter 3, the conditions ensuring existence, uniqueness and global exponential stability of the equilibrium point of interval neural networks with S ?type distributed delays are studied. Applying the idea of homeomorphism, M ?matrix theory and Liapunov functional, the sufficient conditions for global exponential stability of interval neural networks are obtained.In chapter 4, the static neural networks with S ?type distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality technical.