Dynamic Behavior Of A Prey-Predator Diffusion Model With Fear Factor

In this paper,we discuss the effect of anti-predator behaviors due to prey’s fear of predator on the dynamics behavior of the prey-predator diffusion model with Holling-Ⅱunctional response and Allee effect.For the corresponding ordi-nary differential equation model,we study the existence and local stability of all non-negative equilibria,the existence and direction of Hopf bifurcation,and the sta-bility of the bifurcating periodic solution.Moreover,the effects of fear factors on population dynamics are discussed through numerical simulations.For the semilin-ear reaction-diffusion model,we consider the stability of positive equilibrium point,the existence and direction of Hopf bifurcation,and the stability of the bifurcating periodic solution.It is shown that the fear effect can only reduce the predator den-sity around the point of positive equilibrium,but it cannot induce the extinction of predator.The fear factor can also increase the stability of the system by excluding the existence of periodic solutions.