Dynamic Behavior Analysis Of Impulsive Differential Equations With Stage Structure

In this paper, we establish three kinds of population model with impulsive e?ects for the main problems of ecological environment in the breeding and integrated pest management. They are both required in di?erent time of pulse disturbance on system in these three kinds of models. The pulses control strategy of population are studied by using the comparison theory of impulsive di?erential equation,Floquet theory and Lyapunov function constructed method. The full paper is divided into five chapters.The first chapter is introduction. We first briefly introduce the main research work about the situation and the population dynamics. Then some important definitions and preliminary knowledge of impulsive di?erential equations are given.In chapter 2, we investigate a breeding predator-prey system with a Holling II type functional response. Firstly, we introduce the existence of the prey-extinction periodic solution. Then the su?cient conditions of the global asymptotic stability of the prey-extinction periodic solution and the permanence of the system are obtained.Finally, the numerical simulations are given to validate the su?cient conditions.In chapter 3, we study a predator-preys system with impulsive e?ects and delay e?ect. Firstly, in this model, the positive periodic solution of predator extinction is given. Then the su?cient conditions of the global asymptotic stability of the predator-extinction periodic solution and the permanence of the system are obtained by using the theories of impulsive di?erential equations, Floquet theory and Lyapunov function constructed method.In chapter 4, based on integrated pest management strategies,an impulsive functional di?erential system of the pest management with stage structure is established in which we spray of pesticides and release sick pests and natural enemies in a fixed time. The dynamic behaviors of the model are considered. The su?cient conditions of the global asymptotic stability of the susceptible pest-eradication periodic solution and the permanence of the system are obtained by using the theories of impulsive di?erential equations, Floquet theory and Lyapunov function constructed method.In chapter 5, we summarize the thesis briefly.