A Pest Control System With A Functional Response Of Beddington-DeAngelis

In recent years, impulsive differential system models were introduced into the population dynamics and received more and more attention from scholars. Impulsive differential system can fully take into account the effect caused by the instantaneous change on the state variable during the population growth, and it can accurately describe the development process of such systems, therefore it has important the-oretical and practical value in the study of population dynamics. Using impulsive differential system to study pest control problem has become an important aspect in the ecological studies. In the biological control, pest control problem is viewed as an important issue by farmers and the ecology management department. How to pre-vent and control pests effectively and economically has become the common problem concerned by the mathematicians and ecologists. There are three kinds of strategies to control pests:biological pest control, chemical pest control and integrated pest control. Biological control is harmless to the environmental, but it has a slow effect; Chemical pest control has a low cost and a quick effect, but it pollutes the envi-ronment if used for a long time. And integrated pest control is the comprehensive utilization of biological pest control and chemical pest control. For the pest manage-ment, we must consider not only the effective control the number of pests below the certain number, but also the impact on the ecological environment and ecological balance. Therefore, we should choose the pest control management according to the practical situation, we will select biological control (for example spraying pesticide) or chemical pest control (for example throwing in natural enemies) suitably, so that we can control the pest effectively and protect the environment better.In this paper, we establish two kinds of pest control models with Beddington-DeAngelis functional response and impulsive effect. Dynamics behaviors of the models are studied. The research results have certain realistic guiding significance to the agricultural production. The main research contents and results in this thesis are as follows:First, we study a kind of biocontrol pest model with Beddington-DeAngelis functional response and impulsive effect in periodic environment and considering the impact of enemies' density department for model. In a certain time, the number of pests is controlled by spraying pesticide in impulsive form and releasing natural enemies in constant. This paper first proves the positivity and bounded of model's solution and then proves the existence of the pest-eradication periodic solution.Further obtains the conditions of the pest-eradication periodic solution being lo-cally asymptotically stable with Floquet theory and obtains the conditions of the pest-eradication periodic solution of being globally asymptotical stable with com-parison theorem of impulsive differential system, and then proves that the system is persistent when the condition of being locally asymptotically stable is false, and then the dependence of the eventual extinction of the pest on the initial popula-tion number is proved. Finally numerical simulation is carried out to verify the theoretical results.Secondly, we study biological pest management prey-predator model with Bedd-ington-DeAngelis functional response and pest delayed stage structure in periodic environment. To control the population of the pest, we release natural enemies in periodical impulsive form. This paper first proves the positivity and bounded of model's solution. And then, by using the theory of impulsive delay differential equa-tions and the method of comparison, we obtain the conditions of global attractive for the pest extinction periodic solution and the persistence of the system.