Limit Cycles And Stability Of Some Impulsive Differential Equations

This paper mainly discusses the limit cycle and stability of several kinds of discontinuous differential systems.It are consisted of five chapters.In the first chapter,the background and research status of impul-sive differential equations and limit cycle problems are briefly intro-duced.The second chapter is the theoretical basis,which mainly de-scribes the planar impulsive differential system and its solution.In the third chapter,the basic concept of limit cycle of discontin-uous differential system is given.The system where ?r|t=?i=r(?i+)-r(?i),??|t=?i=?(?i+)-?(?i),the derivative is the left derivative at ?i??,?:={?i}.U,V:G?R is continuous and satisfies the local Lipschitz condition for the variable r and 9.The impulsive functions ui,vi:G?R,i?R are continuous.The conditions for the nonexistence and existence of the limit cycle of the system and the judgment theorem for the stability of the limit cycle are obtained.In the fourth chapter,the necessary and sufficient conditions for the existence of limit cycles and the stability theorem of limit cycles are studied.The fifth chapter summarizes the main contents of this paper,and makes a prospect for the next research work.