Dynamics Analysis Of Leslie-Gower Predator-prey Diffusion Model With Fear Factor

In this paper,the dynamic behavior of a diffusive Leslie-Gower predator-prey model with Holling-II functional response,Allee effect and fear factor is investigated.For the corresponding ordinary differential equation model,firstly,the existence and stability of equilibria are analysed.Then by using the bifurcation theory and selecting the appropriate bifurcation parameters,three types of bifurcation in the model are discovered,including transcritical bifurcation,Hopf bifurcation and BogdanovTakens bifurcation.Furthermore,the influence of the fear effect on the stability and bifurcation of the system is analysed.It is shown that the fear effect can reduce the predator and prey densities,but it cannot induce the extinction of predator.And the direction of the Hopf bifurcation,the stability of the periodic solution are investigated,the existence of limit cycles is also discussed.For the semilinear reaction-diffusion model,the stability and Turing instability of positive equilibria,the existence and direction of Hopf bifurcation and the stability of bifurcating periodic solutions are studied.The maximum principle and Harnack inequality are also used to establish a priori estimations of positive steady states for the reactiondiffusion system.Meanwhile,the existence of positive non-constant solutions are discussed by using the Leray-Schauder degree theory.