Abstract: We investigate the Hopf bifurcation behavior of a Leslie-Gower predator-prey model with Holling-type Ⅱ functional response and fear effect.By applying the Hurwitz criterion,we analyze the existence and stability of the equilibrium points of the model.Taking the fear factor as the bifurcation parameter and combining with bifurcation theory,we rigorously prove that the model undergoes a Hopf bifurcation under certain conditions.On this basis,we further discuss the direction of the Hopf bifurcation,the stability of the periodic solutions,and the existence of limit cycles,and completely characterize the complex dynamical behaviors of the model under the fear effect.

Key words: Leslie-Gower model, Hopf bifurcation, fear effect, Poincaré-Andronov-Hopf Bifurcation Theorem