Open AccessStability Analysis of a Fractional-Order Leslie-Gower Model with Allee Effect in Predator
Author(s) -
Emli Rahmi,
Isnani Darti,
Agus Suryanto,
Trisilowati,
Hasan S. Panigoro
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1821/1/012051
Subject(s) - allee effect , hopf bifurcation , extinction (optical mineralogy) , equilibrium point , mathematics , stability (learning theory) , predator , bifurcation , predation , bifurcation theory , statistical physics , mathematical analysis , nonlinear system , ecology , physics , population , biology , computer science , differential equation , demography , quantum mechanics , machine learning , sociology , optics
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.