Qualitative Study Of Several Kinds Of Impulsive Differential Systems

This thesis mainly studies qualitative property of several kinds of plane impul-sive differential systems:the stable property, periodic property and characteristic of phase diagram of the plane linear impulsive differential systems, the periodic property and the existence of the limit cycle of the plane nonlinear impulsive dif-ferential systems, and the phase diagram characteristic of the limit cycle. This thesis uses Matlab software tool draw all kinds of phase diagrams. It is consisted of five chapters.As the introduction, in chapter1, we briefly introduce the historical back-ground and the research of the impulsive differential systems, and the main work of the thesis.In chapter2. we mainly study the stable property and geometrical character-istic of the plane linear impulsive differential systems which have two different real eigenvalue. Firstly, we obtain the system is stable, the infinite diffusion or bound of which sufficient and necessary conditions. Next, we obtain several particular phase diagrams of the system by the analysis of geometrical characteristic of the systems.In chapter3, we mainly study the stable property and geometrical character-istic of the plane linear impulsive differential systems which have plural eigenvalue. Firstly, we consider the real part being zero of the eigenvalue of case, and obtain relevant theorems of which the solution of the system is periodic or stable. Next, we consider the real part being nonzero of the eigenvalue of case, and obtain sufficient and necessary conditions of which the solution of the system is stable.In chapter4, we mainly study the periodic property and existence of the limit cycle of the plane nonlinear impulsive differential systems, obtain two relevant theorems, and discuss all kinds of characteristic of phase diagrams when the limit exists.In chapter5, we summarize the full text and point out some further works.