Qualitative Study On Some Kinds Of Neural Networks

In this paper,applying the method of Lyapunov functional,contraction mapping principle,M-matrix and inequality techniques,the time scales calculus theory. the continuation theorem of coincidence degree theory and the isomorphic mapping theory,we study the global exponential stability to the Cohen-Grossberg BAM-type neural networks,the exponential synchronization of a class of neural network on time scales,the global exponential stability of the Cohen-Grossberg BAM-type neural networks with distributed delays and the existence of periodic solution to shunting inhibitory cellular neural networks(SICNNs) with time-varying delays and variable coefficients.Many existing results reported in the literature are extended or improved.In chapter 1,we introduce the applied background of research on some kinds of neural networks and the main results.In chapter 2,we discuss the the global exponential stability of the Cohen-Grossberg BAM-type neural network with discrete time.Some sufficient conditions of the global exponential stability are obtained,by applying the method of Lyapunov function and the isomorphic mapping theory.These results do not assume the symmetry of the connection matrix,and monotonicity,boundedness and the differentiability of the activation function.In chapter 3,some sufficient conditions are derived to ensure the exponential synchronization of a class of neural network on time scales,using the time scales calculus theory and the Lyapunov functional method.The conditions possess highly important significance and easily checked in practice by simple algebraic methods.In chapter 4,we study the global exponential stability of the Cohen-Grossberg BAM-type neural networks with distributed delays and nonlinear impulses,applying the method of Lyapunov functional,contraction mapping principle,M-matrix and inequality techniques.Some sufficient conditions are obtained to ensure the existence,uniqueness and global exponential stability.This paper improve the usual assumption that the impulsive operators are linear.In chapter 5,we study the existence of periodic solution to shunting inhibitory cellular neural networks(SICNNs) with time-varying delays and variable coefficients. Applying the continuation theorem of coincidence degree theory and differential inequality tecéhnique,we derive a sufficient condition to to ensure the existence of periodic solution to SCINNs.