Qualitative And Bifurcation Analysis Of A Predator-prey Model

The research on the correlation between predator and prey has been favored by many academic researchers for a long time.In order to ensure that the model is more perfect and in line with the practical significance,this paper studies the predator-prey model under two different conditions and obtains the relevant conclusions.In this paper,we first study a predator-prey model with Constant Harvesting Rate and Holling type II functional response.Firstly,the boundedness of the solution of the model is discussed,and we consider the stability and Hopf bifurcation of the model through the extension of the type of equilibrium points.Then the stable points and unstable points are decoupled and analyzed.Finally,the phase diagrams of each equilibrium point and the phase diagrams of the limit loop are obtained by simulation experiments.Secondly,another predator-prey model with Constant Harvesting Rate and fear effect is studied,the existence conditions of the equilibrium point of the model is given,and then expounds and proves the types and stability of the equilibrium point and the Hopf bifurcation problem.Finally,we obtains the unstable limit cycle.This paper display the predator-prey model is vividly by describing the above two models,and the types of equilibrium points and their changing states and stability are expounded and proved.Finally,the model effect is visually displayed through the visual form,and the corresponding stable and unstable limit cycle phase diagrams are obtained through simulation experiments.