Generalization And Application Of Discrete Halanay Inequality

In this paper,we mainly discuss the discrete type Halanay inequalities.On the one hand,we generalize discrete type Halanay inequalities in the literature,and we obtain some new discrete Halanay inequalities.On the other hand,we analyze the stability of several kinds of delay difference equations and neural net-work systems by using discrete Halanay inequalities and constructing suitable V-function.This paper contains four chapters.In Chapter 1,we introduce the historical background,research dynamics of this article and the main works of this paper.In Chapter 2,we establish some new generalized forms of the discrete Halanay inequality.We improve the hypothesis in the literature,and then use this in-equality to analyze the stability of the trivial solution of several delay difference equations.Finally,several illustrative examples are given to prove the availability of the obtained results.In Chapter 3,we study conditions of the impulsive discrete BAM neural networks with time-varying delays the global asymptotical stability.The main method is to establish a new impulsive discrete Halanay inequality and construc-t a suitable V-function.Then we get the sufficient conditions to guarantee the global asymptotical stability of this system.Finally,an illustrative example are given to prove the availability of the obtained results.In Chapter 4,we correct a wrong discrete Halanay inequality in the litera-ture.Firstly,we point out the errors in the literature and analyze the causes of the errors.Then we give the corrected theorem and prove it.