Qualitative Study Of Several Kinds Of Second Order Non-linear Impulsive Systems

This thesis mainly studies qualitative property of several kinds of second order non-linear impulsive systems. It is consisted of five chapters.In Chapter 1, the background and history of impulsive differential equation and non-linear impulsive differential systems, and the main results of this work are stated.In Chapter 2, we discuss the stability and the boundedness of a Lotka-Volterra competitive system with infinite delays. First of all, we consider the property of the impulsive competitive system’s zero solution is related to the corresponding non-impulsive competitive system’s zero solution. By using Lyapunov function, we get nonzero solutions’s the stability of the Lotka-Volterra competitive system with infinite delays.In Chapter 3, we consider the permanence and partial of a predator-prey system by using the comparison principle of impulsive differential system. And the sufficient and necessary conditions for the permanence and partial of this system are obtained.In Chapter 4, we discuss the more general impulsive differential system. By using Lyapunov function, we obtain the sufficient condition of the impulsive control to obtain the stability of the solutions.In Chapter 6, we summarize the full thesis and pointed out the further re-search work.