The Qualitative Analysis Of Predator-Prey System With Harvesting Rate

Predator-prey system with harvesting rate is studied by qualitative analysis,in order to predict the development and change of population and to analyze the capture behavior's effect on the population.We can decide how much capture quantity is to maintain the balance of ecological system and to satisfy the need,when capture quantity reaches the top.From these facts,it is very important that the system with harvesting rate relates to the problem of resource continuable development. Since 1979,much research has been done on predator-prey system with harvesting rate as well as the analysis of qualitative and stable properties. Besides,the properties of equilibrium,local stability and globally stability are also discussed. On the basis of work which has been done,this paper makes further study on predator-prey system with harvesting rate. Firstly, it discusses Holling â…¢functional response predator-prey system with density restriction.It uses general qualitative analysis methods,such as the boundary of solutions and the existence of limit cycles.Then this paper studies the general functional response model with linear harvesting,by constructing Lyapunov function and concludes that the unique positive equilibrium is globally stable. Secondly,concerning Kolmogorov model and generalized Kolmogorov model with variable harvesting rate,this paper utilizes Dulac function to judge the existence of the close path curve,Bendixson cycle region to judge the direction of path curve,and constructs Lyapunov function to judge the global stability,in order to fit the general models. Thirdly,as for three-dimensional population model with harvesting rate,it discusses the qualitative problem of a functional response model by variation matrix and Routh-Hurwitz criteria,and concludes the existence of the equilibrium and the sufficient and necessary condition of populations. Finally,we carry out the simulated plot with the help of Maths software Mathematica and MathCAD which make the intuitional realization of the models.