The Research Of Several Pests Control Models With Impulsive Effect

This dissertation based on the simplest SI model, the dynamic of pests control models with Logistic growth curve are established. The focus of this dissertation is to study several types of pests control models with impulsive effect. We discuss the stability of the semi-trivial periodic solution and permanence of the given systems. By using the theory of impulsive dynamics, we investigate dynamics for impulsive systems. Moreover, the impulsive dynamical systems are simulated by Maple. The dissertation is divided into three parts.In Chapter 1, the goal, significance and background of the dynamics research in impulsive differential dynamical system, as well as the work of the dissertation are introduced. Moreover, the basic theory of impulsive differential dynamical system and definitions we need in this dissertation are presented. Also, the fixed time impulsive dynamical systems, the moments of impulsive dynamical systems and the pulse autonomous equations, the Floquet theorem of the linear periodic impulsive differential equations, the comparison theorem and stability theory of the impulsive differential equations are presented.In Chapter 2, the model with natural mortality and impulsive effect for pest control are given. We obtain the existence of the periodic solution by using impul-sive comparison theorem. The sufficient conditions of global asymptotic stable of the semi-trivial periodic solution and the permanence of the system are given by the Lyapunov function. Also, numerical simulations suggest the correctness of the conclusion. In addition, we analyze the bifurcation of the semi-trivial periodic so-lution, obtaining the stability of the positive periodic solution. Finally, we discuss the effectiveness of the strategy of integrated pest management of this system.In Chapter 3, we give the model of pest control model with impulsive diffusion between two patches. We obtain the existence of the periodic solution by using impulsive comparison theorem. The sufficient conditions of semi-trivial periodic solution and the permanence of the system are obtained by using Lyapunov func-tion. Numerical simulations are given to support the correctness of the conclusion obtained in this paper.