The Study On Predator-prey System With Impulsive Effects

In this paper, by use of the theory on impulsive differential equation, we study some predator-prey systems and discuss the permanence and stablity of population ecological models. The article is divided into three chapters.In Chapter 1, We introduce some knowledge of biology mathematics, the main works and some prelimineries.In Chapter 2, we study predator-prey system with impulsive effects. At first, the article dis-cussed a predator-prey system with the Beddington-DeAnglis functional response, controlled the pest by using the stratege which is periodically releasing predator (natural enemy) and periodi-cally capturing prey (pest). By using the Floquet theory of impulsive equation and comparison theorem, we obtain sufficient conditions of the locally asymptotical stability of prey-extinction periodic solution and the permanence of the system. Next, we consider a predator-prey model with Leslie-Gower Holling II type schemes and Gomportz which has periodic harvesting for the prey and stage-structured for the predator. By use of the discrete dynamical system deter-mimed by the stroboscopic map and the comparison theory of impulsive equation, we obtain some corresponding threshold conditions which guarantee the globally asymptotical stability of predator-extinction periodic solution and the permanence of this system. At last, based on the integrated pest management program, a predator-prey system with impulsive effect and Ivlev functional response is studied. By using the Floquet theory of impulsive equation and comparison theorem, sufficient conditions for the population to be extinct and permanence are given.In Chapter 3, a predator-prey model with sexual favoritism is considered which has stage-structure and Holling II functional reponse. conditions of permanence for the system were obtained by constructing inequality. the global stability of the periodic solution were approved by Liapunov method.