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

Rina Exviani,Wuryansari Muharini Kusumawinahyu,Noor Hidayat

doi:10.21776/ub.jels.2018.008.02.10

Rina Exviani, Wuryansari Muharini Kusumawinahyu + Show 1 more

Open Access

https://doi.org/10.21776/ub.jels.2018.008.02.10

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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

Highlights

Lotka-Volterra model was firstly introducedLotka in 1925 and Volterra in 1926 [1]
The model is known as LeslieGower Predator-Prey Model
The predator-prey model by Leslie-Gower model with omnivores is more concrete in this case

Summary

INTRODUCTION

LotkaVolterra’s study has produced a simple model of predation or interaction between two species in an ecosystem. They have introduced classical Lotka-Volterra model, which is currently developed by researchers [2]. In 1948, Leslie discussed Lotka-Volterra model and found impossibility in a model, which is infinity in predator growth [3]. Leslie-Gower two dimension models as: species are omnivores This model is constructed by assumming there are just three species in such an ecosystem. In 2015, Andayani and Kusumawinahyu [4] a three species predator – prey model, the third In this model, and the density of prey, predator, and omnivore populations, respectively. Leslie-Gower with omnivores which is modified by Lotka-Volterra model with omnivore. Gower model with omnivores is more concrete in this case

Existence Requirement

RESULT

This stability analysis uses the criteria of

Simmulation IV

CONCLUSION