Abstract: By using  the eigenvalue theory of differential equations, Poincare-Bendixson ring theorem and Hopf bifurcation theory, we  analyzed the predator-prey model of Holling-Ⅱ with fear effect and modification, gave the stability of the equilibrium point of the model, and proved that the model had stable limit cycles and Hopf bifurcations appeared at coexistence equilibrium points. The results show that the fear effect and the modified Holling-Ⅱ function have significant effects on the stability of the system.

Key words: predator-prey model, fear effect, modified Holling-Ⅱ functional response function, stability, Hopf bifurcation