On Exponential Stability Of Several Classes Of Neural Networks

In this paper, we consider the global exponential stability for several kinds neu-ral networks with variable delays.According to the trait of the different neural net-works,constructing suitable Lyapunov functions,using M-matrix theory, we discuss the existence,uniqueness of the equilibrium point,the global exponential stability and the periodic for neural networks.Meanwhile,we obtain the sufficient conditions for the existence,uniqueness of the equilibrium and the periodic solution.There are four chapters in this paper:In the first chapter, some background knowledge of several classes neural net-works systems are introduced, and the preliminary knowledge which is necessary in the paper is given.In the second chapter, the Cohen-Grossberg nerual networks with s-typed dis-tributed delays and impulses. Applying the method of Lyapunov functions,M-matrix theory and the Rauzumikhin technique.A sufficient criterion of stability of networks has also been obtained.In the third chapter, global exponential stability and periodicity of a class of cellular nerual networks with variable coefficients and delays are investigated.By applying Lyapunov function and inequality analysis,Poincare mapping, sufficient conditions are obtained.In the fourth chapter, we consider the exponential stability of BAM neural networks with distributed delays and impulses.Based on Brouwer fixed point theo-rem,we investigate the stability of the equilibrium point for BAM neural networks.