Discrete prey-predator model with fear effect and strong Allee effect

Abstract

The rich dynamic properties of a discrete prey-predator model with fear effect and strong Allee effect are studied. The piecewise constant argument method of differential equation is used to discretize the system, and the existence of equilibrium point of discrete system is obtained. The stability conditions of the equilibrium points of the discrete prey-predator model are obtained by the stability theory of the dynamic system. The existence and direction of the Neimark-Sacker bifurcation at the positive equilibrium point are analyzed by using the bifurcation theory. The local asymptotic stability and bifurcation theory of the positive equilibrium point are verified by numerical simulation, and it is proved that the system can be stabilized by appropriately reducing the maximum environmental capacity of the prey.

Keywords

• fear effect
• strong allee effect
• stability
• neimark-sacker bifurcation