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

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.