The Stability Analysis Of Two Classes Of Delayed Neural Networks

Due to the broad spectrum of applications in areas such as optimization, signal and image processing, solving nonlinear algebraic equation, pattern recognition, and associative memories, artificial neural networks have been fully developed. Because the information processing capability of a neural network is determined by its dynamic behavior, the study of dynamic properties of neural networks has been one of the most important topics of research in this area.This thesis addresses the stability of delayed neural networks. First of all, the thesis briefly reviews the fundamental knowledge, the history and the state-of-the-art of stability of neural networks. On this basis, the thesis makes the following contributions.1. A class of neural networks with distributed delays and impulses is studied. First, by calling the Banach fixed-point theorem, a criterion for the existence and uniqueness of an equilibrium of such neural networks is established. Second, by combining the Lyapunov functional method and some inequality techniques, accompanied with the introduction of a set of parameter, we give a sufficient condition of the global exponential stability of the unique equilibrium for the above mentioned systems; it should be mentioned that this condition is independent of the associated delays. This condition is an extension of some previously known results.2. A class of discrete Hopfield neural networks with delays is investigated. First, under proper conditions, the existence of an equilibrium is shown by using the Brouwer fixed-point theorem. Second, a sufficient condition of global exponential stability of such networks is set up. Finally, this criterion is justified via numerical examples and simulation experiments.