Asymptotic Behavior,Periodic Solution Of Impulsive Differential Equations And Its Applications In Population Ecology

This paper is concerned with asymptotic behavior and periodic solutionof impulsive differential equations.In Chapter 1, for a class of impulsive differential equation with delay, we spread the Yoshizawa's theory about periodic solutions. By it a sufficient condition is gained for the existence of periodic solutions of the system with nonlinear perturb.In Chapter 2, by using a class of piecewise "continuous Lyapunov function and the method of analysis, we study existence, uniqueness and stability of impulsive Volterra intergro-differential equations.Chapter 3 first obtains some criterions about the stability, asymptotic stability and exponential stability of linear differential equations and its perturbed systems with impulse by using impulsive inequality. Then we study the existence of periodic solutions for a class of nonlinear impulsive differential equation.In Chapter 4, For the two species periodic predator-prey system with impulse, we discuss the persistence , the existence and uniqueness of periodic solution, and the global asymptotic stability.