Study On Population Dynamic Models With Impulsive Effects

The study on population dynamic model has been widely concerned because of the practical significance in the biological field. In recent years, bas-ed on using continuous or discrete equations to study population models, many scholars estabilished population dynamic model with impulsive effects in order to describe the practical problems more appropriate.Integrated pest managenment (IPM) is a very suitable method to managing pests by combing biological, cultural, physical and chemical tools in a way that minimize economic, health and protecting environmental. It needs to study further in modeling and analyzing the population dynamic by impulsive system. Consequently. the population models with impulsive effects need to be optimiz-ed. In this dissertation, population dynamic models are studied to consider population controls by means of the theory and methods of impulsive differe-ntial equations.Capter 1 surverys the history and development of population dynamic models. The main methods and results of impulsive systems are introduced as well. The brief contents about this paper are given as follow.In Capter 2. the basic theory of impulsive systems systems are introduced. The definition and theory be used for later are given in detail.Capter 3 studies the dynamic behaviors of the predator-prey of Holling typeⅡfunction response system with impulsive effects. On the theory of controlling pest, the releases of predators are impulsive. We consider changing some coefficients to make the existing model better. By using the theory of the differential eqution, it is shown that it has a positive equilibrium. The sufficient conditions that the equilibrium point is locally asymptotically stable are given. The extinction and permanence of the system is studied via the Floquet theory and comparison theory. It is shown that the pest-eradication periodic solution is globally asymptotically stable and system is permanent.A predator-prey model of one-predator two-prey concering impulsive effects is analyzed in Capter 4. After optimizing the existing model, the dynamic behaviors of this impulsive system are studied. Using Floquet theory and small amplitude perturbation method, we give the sufficient conditions that the pest-eradication periodic solution is globally asymptotically stable. Then we prove it. Finally, we analyze the permanence of the system.In Capter 5, a predator-prey model of two-predator one-prey concering impulsive effects is estabilished and discussed. Using biological control, we control the population of pest. We show that there exist the sufficient conditions of a locally asymptotically stable pest-eradication periodic solution with the impulsive effects. The sufficient condition for the permanence is also given.Finally, a conclusion of the dissertation and some future research topics in the field are given in Capter 6. The idea of population dynamic with impulsive and switching effects is considered, and the numerical simulations are given. The simulation results show the feasibility of this idea.