A Dynamics Behaviour of Two Predators and One Prey Interaction with Competition Between Predators

9th Annual Basic Science International Conference 2019

自然科学（总论）

Savitri, Dian^1^3 ; Suryanto, Agus^2 ; Kusumawinahyu, Wuryansari M.^2 ; Abadi^3

Faculty of Mathematics and Science, Brawijaya University, Malang, Indonesia^1

Department of Mathematics, Faculty of Mathematics and Science, Brawijaya University, Malang, Indonesia^2

Mathematics Departement, Faculty of Mathematics and Science, Universitas Negeri Surabaya (Unesa), Surabaya, Indonesia^3

关键词: Asymptotically stable;    Equilibrium point;    Interior point;    Leslie-gower;    Local stability analysis;    Predator populations;    Predator-prey modeling;    Research focus;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052069/pdf
DOI  :  10.1088/1757-899X/546/5/052069

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

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.