Modified Leslie-Gower Model with Holling Type I Functional Responses and Cannibalism in Prey

Abstract

The predator-prey model is the mathematical model that describes the interaction behavior between prey and predator. This research discusses the modified Leslie-Gower model by considering the cannibalism behaviors of the prey that contains Holling type I response function, which is a predator with passive characteristics. The stability analysis stage includes determining the system's solution in the form of an equilibrium point, analyzing the local stability of each equilibrium using eigenvalues, and numerical simulation to synchronize the analysis results. Numerical simulations visualized in phase portraits with Python software. The results of the local stability analysis of the system obtained four equilibrium points, namely, equilibrium points  are unstable while is asymptotically stable with certain conditions. The results of numerical simulations show that only the equilibrium point  which is asymptotically stable when the environment carries capacity parameters (e=2.1). Meanwhile, when e=2.878 then, only is asymptotically stable. In this research also using two different initial values, it is concluded that whatever the initial value used, the system solution always converges to the equilibrium points  dan . Changes in environmental carrying capacity affect the dynamics of system solutions.