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

Authors

  • Rina Exviani Magister Mathematics of Brawijaya University
  • Wuryansari Muharini Kusumawinahyu Departement of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya.
  • Noor Hidayat Departement of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya.

DOI:

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

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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Published

2018-07-26

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Articles