Study On The Dynamics Of A Predator - Prey Pulsed System With Harvesting

In recent years, the prey-predator model plays a more and more important role in the ecological problems. How to adjust the population more effectively and to maintain benign development have a very important ecological significance and application value. Nowadays, people solve problems in the population dynamics model by using the mathematical theory and methods, and an abstract complex dynamic phenomena can be converted to the mathematical model. Recent years, many scholars do a lot of research for all kinds of population model dynamic behavior, but the research about the population model dynamic behavior with impulse is very less. By using mathematical analysis knowledge and differential equation qualitative theory method,in this paper, a harvesting predator-prey model with Hassell-Varley type functional response and impulsive effects is studied, the dynamic behavior of the model and some value results are obtained. At the same time, by using the Matlab, we get the numerical simulation that holds for the main results.This paper consists of five chapters. In chapter l,we introduce the background knowledge, research significance, current situation in domestic, overseas of the model and the main work in this paper. In second chapter, we introduce preparation knowledge. It consists of basic knowledge for impulsive differential equations, the concept about stability of the solution for differential equation and the fixed point theory for studding the periodic solution. The third chapter gives the main results. We study dynamic behavior of the model, that is periodicity, persistence, stability. Then, by using the basic knowledge of impulsive differential equations and the fixed point theory based on monotone operator, we get some simple sufficient conditions for the existence of at least one positive periodic solution of the model. The existence result of this paper implies that the functional response on prey does not influence the existence of positive periodic solution of the model which improves the recent results. Furthermore, by applying the comparison theorem in impulsive differential equations and Lyapunov function we get sufficient conditions for the persistence of the model.Finely, by using the method of Lyapunov functional we investigate the global attractivity of the model. In chapter4, we give two examples and numerical analysis to illustrate the feasibility and effectiveness of the main results. Chapter5for the conclusion and outlook, we summarize the main work in this paper and make a further outlook about the issue which needs to be considered in the future.