| So far, many impulsive equations modeling the process of population ecology have been studied. Most of such research is focused to impulsive differential equations at fixed moments. However, sometimes, chemicals must be sprayed or natural enemies be released in time to protect the growth of the crop when the amount of pests reaches a critical value. Therefore,the impulsive fixed-time control may result in reduction of crop yield. To avoid this situation, this paper investigates complex behavior of a Beddington-DeAngelis system with continuous harvesting for prey and impulsive state feedback control strategy instead of impulsive fixed-time control.In this paper,a Beddington-DeAngelis prey-predator system with continuous harvesting and impulsive state feedback control is proposed.The main contents are as follows:The first chapter is an introduction that introduces the development and research achievements of the biomathematics and the development of the impulsive differential equations in biomathematics. This chapter also introduces the research significance of this issue and the main research work of this paper.The second chapter is basic knowledge that provides a solid theory foundation for researching later in this article.In the third chapter we discuss the predator-free periodic solution of a Beddington-DeAngelis system with impulsive state feedback control via establishing two Poincare maps. And then we prove the existence and stability of the predator-free periodic solution.In addition,the condition of bifurcation is proposed by using the theory of Floquet multiplier. When the predator-free periodic solution loses its stability,the existence and stability of nontrivial periodic solution is also established. The forth chapter is a numerical simulation that shows the feasibility and the superiority of this model.The last chapter is conclusion. This chapter summarizes all fo my work and indicates the problems that need research deeply. |
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