The Study Of Effects Of Impulses On A Periodic Single Species System

In this thesis,some theories and approaches related to impulsive differential equations and numerical simulations are used to investigate dynamical behaviors of an impulsive periodic single-species system including the permanence,global attractivity of positive solution,existence and global asymptotic stability of positive periodic solution.The whole thesis is divided into three chapters.The first chapter introduces concisely the historical situation and the present development of relevant subjects about impulsive population dynamics as well as the main work done in this thesis.Also,some preliminaries on impulsive differential equations are given.In the second chapter,by using the theories of impulsive differential equations and Lyapunov function the permanence and global attractivity of a periodic single species with constant impulse are established.An example and its numerical simulation are also given.In the third chapter,we continute to investigate the above periodic single species system with linear impulsive perturbations.By using the theories of impulsive differential equations,Brouwder fixed points theorem and Lyapunov function,a good understanding of the existence and global asymptotic stability of positive periodic solutions is gained.An example and its numerical simulation are also given.