Dynamic Analysis of Modified Leslie-Gower the Predator-Prey Model with Fear Effect, Additional Food, and Prey Refuge

Hanifa Febriana Putri; Dian Savitri

doi:10.37905/euler.v14i1.37804

Dynamic Analysis of Modified Leslie-Gower the Predator-Prey Model with Fear Effect, Additional Food, and Prey Refuge

Hanifa Febriana Putri, Dian Savitri

Abstract

This study discusses a Leslie–Gower prey-predator model incorporating three behavioral mechanisms: the fear effect on prey, additional food for predators, and prey refuge, with predation rate of predators using the Holling II response function. The objective of this research is to analyze the system dynamics through stability analysis of equilibrium points and the bifurcation associated with the predator attack rate parameter. The analytical results indicate that the model admits five equilibrium points, namely the extinction of both populations (E1), prey extinction (E2), predator extinction (E3), and two coexistence equilibrium points (E4 and E5), where the existence of the interior equilibrium points depends on the values of the system parameters. The prey extinction equilibrium point and the coexistence equilibrium points are asymptotically stable under certain conditions. Computational validation was performed through numerical simulations. Furthermore, variations in the predator attack rate parameter reveal the presence of bistability as well as transcritical and saddle-node bifurcations that lead to changes in the stability of the equilibrium points.

Keywords

Model Leslie-Gower; Fear Effect; Prey Refuge; Additional Food; Holling type II

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DOI: https://doi.org/10.37905/euler.v14i1.37804