Research On The Stability And Branching Of Several Types Of Predator Models

In this paper,we mainly study the effects of functional response,refuge and harvest on the stability and bifurcation of a predator-prey system.We use characteristic theory,Hurwitz criterion and the normal form theory to analyze the stability of the equilibria and bifurcation.Some new conclusions have been obtained after studying several kinds of predator-prey system.The paper includes four sections.Chapter 1 The background of predator-prey system are reviewed.According to the relationship between some important factors,we establish the delayed differential equations and study its properties.Chapter 2 We study a double delay predator-prey model with stage structure for prey and Ivlev-type functional response.In this section,we prove the existence and the local stability of equilibria for the model without delays.For the double delay predator-prey model,we study the existence of Hopf bifurcations by discussing the different cases of time delays.Chapter 3 We study predator-prey model with prey refuge providing additional food to predator.In this section,we consider the influence of refuge and additional food.We derive the stability and the existence of Hopf bifurcations at equilibria,and the period solutions.Chapter 4 We study a delayed predator-prey model with reserve area for prey and harvest.In this section,we study the stability and bifurcation of the model.We prove the bound-edness of the solution and existence of the equilibria,and discuss the existence of Hopf bifurcation at different delay parameters.