Open AccessA Dynamics Behaviour of Two Predators and One Prey Interaction with Competition Between Predators
Author(s) -
Dian Savitri,
Agus Suryanto,
Wuryansari Muharini Kusumawinahyu,
Abadi Abadi
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/546/5/052069
Subject(s) - extinction (optical mineralogy) , predator , predation , equilibrium point , competition (biology) , population , stability (learning theory) , stability theory , ecology , mathematics , biology , physics , mathematical analysis , computer science , nonlinear system , paleontology , demography , quantum mechanics , machine learning , sociology , differential equation
This research focuses on the dynamical of a Leslie-Gower predator-prey model with competition on predator populations. The model represents an interaction between one prey and two predator populations. The analysis shows that there are four equilibrium points, namely the extinction of predator populations point, the extinction of the first predator population point, the extinction of the second predator and the interior point. The existence of the interior equilibrium point is investigated by using Cardan criteria. Local stability analysis shows that both predator populations have never been extinct together. The second and third equilibrium point is local asymptotically stable under some conditions. Numerical simulations are carried out to investigate the stability of the interior point as well as to show that more than one equilibrium point may be asymptotically stable together for a set of parameter.