Dynamical Analysis of Predator-Prey Model Leslie-Gower with Omnivore

Rina Exviani, Wuryansari Muharini Kusumawinahyu, Noor Hidayat

Abstract


This article discussed a dynamical analysis on a model of predator-prey Leslie-Gower with omnivores which is modified by Lotka-Volterra model with omnivore. The dynamical analysis is done by determining the equilibrium point with its existing condition and analyzing the local stability of the equilibrium point. Based on the analysis, there are seven points of equilibrium. Three of them always exist while the four others exist under certain conditions. Four points of equilibrium, namely and are unstable, while the others three equilibrium point are local asymptotically stable under certain conditions. Moreover, it’s also conducted numerical simulations to illustrate the analytical. The results of numerical simulations agree with the results of the dynamical analysis.

Keywords: local stability, omnivore, predator-prey models, the equilibrium point


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