Effects Of Harvesting Rate And Diffusion On The Stability And Hopf Bifurcation Of A Predator Prey System

In recent years, the research on the problem of the branch of the predator-prey system with harvesting rate, time lag and functional response function has become an important research topics in the biological population system. In this paper, the stability and bifurcation of two kinds of predator-prey systems with harvesting rate and time delay are studied by using the qualitative and stability theory and bifurcation theory of ordinary differential equations.In the first chapter, through access to a large number of relevant information, we reviewed the research functions of predator-prey systems, trends and issues with harvesting rates and with Delay and Functional Response, and put forward the main work of this paper is to study.In the second chapter discusses the harvesting rates of biological predator-prey systems. Firstly, using the qualitative and stability theory to study the boundedness of the solution and the properties of the positive balance point, and concluded that the system has a positive balance point when the harvesting rate of prey and predator meets certain conditions, and obtain sufficient conditions for the stability of positive balance point and limit cycle existence. Followed by Matlab software to simulate, validate the conclusions are reasonable and feasible. The results obtained are extended to the qualitative analysis of the two species predator prey model of Du Haiwei et al.In the third chapter, the predator-prey system with time delay and diffusion term and Holling-II is studied. Firstly, using the theory discussed the balance point state, focus on exploring the effect of diffusion of the balance point, and gets the diffusion term doesn't affect the system's non-negative and bounded but affect the existence of the balance point; Secondly, using bifurcation theory gets that the balance point is asymptotically stable when no delay and the terms about the existence of Hopf bifurcation in the vicinity of the positive balance point. The results of this chapter enrich the related research theories of the diffusion term in the predator prey system.