The Global Exponential Stability Of Several Kinds Of Neural Networks

Due to the broad spectrum of applications in optimization, signal processing, image processing, solving nonlinear algebraic equation, pattern recognition, associative memories and so on, the artificial neural networks (ANN) have been fully developed . Because the functions in information processing is determined by the dynamic quality of the artificial neural networks , it is necessary to investigated the dynamic qualities such as stability,oscillation, bifurcation and chaos and so on . Especially, in the applications of optimization, neural control, signal processing and pattern recognition, the global asymptotic stability has become the core problem in the research in order to avoid the spurious response or local minima.In the realization of electronic neural networks, time delays are likely to 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 the dynamic behavior of the two kinds of ANN models with delays and without delays have been investigated in this thesis.The fundamental problems of the ANN dynamic models are the following: 1. the existence of equilibrium; 2. the attractivity; 3. the stability. In this thesis, the feasible criteria of several ANNs to criticize existence of the unique global exponential stable equilibrium.In this thesis, therefor, a new method of analyzing the globally exponential stability of Hopfield Neural Networks is presented in chapter 1, and the criterium of the globally exponential stability of Bidirectional Associative Memory Neural Networks with Varying Time Delays is also acquired in chapter 2. Besides, a new lemma about the Halanay Differential Inequality is obtained and a new method-system approximation method is firstly introduced, by which the globally exponential stability of the cellular Neural-Network and Bidirectional AssociativeMemory Neural-Network Models with S-type distribution delays is investigated in chapter 3. All of those above have generalized and strengthened the results introduced by many other authors.