A Fractional Order Predator-Prey Model with Strong Allee Effect and Michaelis-Menten Type of Predator Harvesting

Abstract

Allee effect and harvesting are two important objects in the ecological system since they are directly connected to the existence of biological resources. Here, we study the impact of the strong Allee effect in prey and Michaelis-Menten type of harvesting in predators on the dynamics of a Gause-type predator-prey model. To involve the influence of the memory effect, the Caputo fractional-order derivative is applied. As a preliminary analysis, we obtain three types of equilibrium points namely the origin point, a pair of the predator extinction points, and the co-existence point. Some interesting dynamics are shown such as the local stability for each equilibrium point, the existence of transcritical bifurcation around the predator extinction points, and the occurrence of Hopf bifurcation around the co-existence point. Furthermore, some numerical simulations are performed to reinforce the theoretical findings.