Stability Analysis of a Fractional-Order Leslie-Gower Model with Allee Effect in Predator

In this paper, the dynamics of a fractional-order Leslie-Gower model with Allee effect in predator is investigated. Firstly, we determine the existing condition and local stability of all possible equilibrium points. The model has four equilibrium points, namely both prey and predator extinction point, the prey extinction point, the predator extinction point, and the interior point. Furthermore, we also show the dynamic changing around the interior point due to the changing of the order of the fractional derivative, namely the Hopf bifurcation. In the end, some numerical simulations are demonstrated to illustrate the dynamics of the model. Here we show numerically the local stability, the occurrence of Hopf bifurcation, and the impact of the Allee effect to the prey and predator densities.