Study On The Dynamics Of Pest Control Models With Holling Ⅱ Response

In agricultural production, the damage of pest to crops is a problem that can not be ignored. To ensure the yield and quality of crops, a variety of methods are used to prevent and control pest, and chemical control and biological control are common ones. Chemical control is mainly spraying pesticides to control pests, and biological control is mainly through the release of natural enemies to control pests. Many scholars do a lot of research on pest control by using mathematical models to simulate the process of biological control and chemical control. Firstly, this paper takes the Holling Ⅱ predator-prey model as an example and generalizes the current pest control methods; Secondly, considering the continuous process of spraying pesticide and releasing natural enemies, a threshold control strategy is taken in this paper, and a pest control Filippov model with Holling Ⅱ response is proposed. The specific research contents are as follows:In Chapter 1, it introduces some definitions, lemmas and preliminaries about this paper.In Chapter 2, the dynamics of a continuous Holling Ⅱ predator-prey model is given including the sufficient conditions of locally asymptotic stability and globally asymptotic stability of the positive equilibria.In Chapter 3, it gives a state-dependent Holling Ⅱ pest control model and introduces the existence of order one periodic solution of such model.In Chapter 4, based on impulsive differential equation, a Holling Ⅱ integrated pest management model with impulse at fixed time in a period is firstly established, and the conditions of locally asymptotic stability of pest-eradication periodic solution and permanent of system are given; Secondly, a Holling Ⅱ integrated pest management model with impulse and differently frequent control is proposed. With spraying either more or less frequently than the releases, the conditions of locally asymptotic stability and global attractiveness of pest-eradication periodic solution are obtained.In Chapter 5, on the basis of the previous four chapters, it improves the pest control model and takes integrated pest management method(IPM). Taking the pest population as the control index, a pest control Filippov model with Holling Ⅱ response is set up, and the dynamics of such model are systematically studied including sliding mode domain, existence of real equilibria and virtual equilibria and existence and globally asymptotical stability of pseudo-equilibrium. By numerical simulation, globally asymptotical stability of real equlibria are also obtained.