Of Impulsive Differential Equations

This paper investigates the stability of a class of impulsive delayed neural networks, impulsive delayed cellular neural networks and impulsive delayed Cohen-Grossberg neural networks. The thesis consists five chapters.Chapter 1 gives an introduction to some basic concepts of impulsive differential equation including Lyapunov function, Dini derivative, stability definition and stability theory of differential equation.In Chapter 2, the stability for a class of impulsive delayed neural networks is investigated. By utilizing Lyapunov function, the uniform stability is obtained.In Chapter 3, the impulsive delayed cellular neural networks are considered. By using the method of Lyapunov functions, M matrix and differential inequality, some sufficient conditions for ensuring global exponential stability of these networks are obtained. The results generalize the previous delayed cellular neural networks without impulsive.Chapter 4 investigates the impulsive delayed Cohen-Grossberg neural networks. Global exponential stability is considered by Lyapunov function, impulsive differential inequality and the well-known Young's inequality and Holder's inequality. The proposed condition generalizes some previous results in the literature.In the last chapter, we summarize the content of the article, and go along expecting discussion.