Hopf bifurcation of a delayed predator-prey model with Allee effect and anti-predator behavior

This paper proposes a diffusive predator-prey model with Allee effect,time delay and anti-predator behavior.First,the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied.Using the normal form and center manifold theory,the formulas which can determine the direction,period and stability of Hopf bifurcation are obtained.Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations,and anti-predator behavior can greatly improve the stability of the coexisting equilibrium.