Abstract: The author considered a class of delayed predator-prey model with fear effect. Firstly, by using the characteristic equation and Lyapunov-LaSalle invariance principle, the global asymptotic stability of the boundary equilibrium was proved when R(τ)≤1. Secondly, by using the Hopf bifurcation theory of delay differential equation, the author discussed the stability of the coexistence equilibrium point and the existence of the global Hopf bifurcation when R(τ)>1, and obtained the results that fear effect and delay affected the stability of the system. Finally, the correctness of the theoretical results was verified by numerical simulations.

Key words: fear effect, delay, Lyapunov-LaSalle invariance principle, Hopf bifurcation