Study On Holling Predator-prey System Incorporating Prey Refuges And Harvesting

The prey-predator model is one of the important issues in today's ecology theory. In this paper, we mainly study the prey-predator model with prey refuge and harvesting. We discuss that prey refuge and the capacity of independent fishing have effect on the density of prey and predator.In Chapter 2, we study the dynamics of prey-predator with Holling I, Holling II and Holling III functional response respectively. Firstly, we discuss the existence, stability and global stability of equilibria for the three types systems. Then, through numerical simulations and analyzing the corresponding results, we obtain that the harvesting effort E1 and E2 and prey refuge may increase the stability of the inner equilibria of the system.In Chapter 3, we investigates the dynamical behavior of a Holling type predator-prey system incorporating refuges using by prey and independent harvesting in their species. The existence of bionomic and optimum equilib-rium of the system is ex-amined. The global stability of equilibrium points in the first quadrant, equilibrium density values, and the long-term persistence of the populations have been consid-ered. The optimal harvesting policy is studied. Some numerical simulations are also carried out.By analyzing the stability of the prey-predator model with Holling functional response, we find the harvesting effort E1 and E2 and prey refuge may increase the stability of the inner equilibria of the system. Here, stabilization or increase of stability refers to cases where a conminunity equilibrium point changes from the unstable state surrounding at least limit cycle to the globally asymptotic-ally stable state due to changes in the value of the parameter E1 and E2.The results show that the parameter conditions under which each of these equilibrium solutions are expected depend strongly on the mode of harvesting.