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Dynamical Behavior of a Modified Leslie–Gower One Prey–Two Predators with Competition

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  • Dian Savitri

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Surabaya, Surabaya 60231, Indonesia)

  • Agus Suryanto

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia)

  • Wuryansari Muharini Kusumawinahyu

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia)

  • Abadi

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Surabaya, Surabaya 60231, Indonesia)

Abstract

We study the dynamics of a modified Leslie–Gower one prey–two predators model with competition between predator populations. The model describes complex dynamics in the permanence, global stability and bifurcation. It is shown that there are eight possible equilibrium states. Two equilibrium states, i.e., the extinction of all of the species state and the extinction of both predators state are always unstable, while the other equilibrium states are conditionally locally and globally asymptotically stable. We also analyzed numerically the effect of competition between predators. Our numerical simulations showed that the competition rate of the second-predator may induce the transcritical bifurcation, the saddle-node bifurcation as well as the bi-stability phenomenon. Such numerical results are consistent with the analytical results.

Suggested Citation

  • Dian Savitri & Agus Suryanto & Wuryansari Muharini Kusumawinahyu & Abadi, 2020. "Dynamical Behavior of a Modified Leslie–Gower One Prey–Two Predators with Competition," Mathematics, MDPI, vol. 8(5), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:669-:d:351395
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    References listed on IDEAS

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    1. Charles Raymond & Alfred Hugo & Monica Kung’aro, 2019. "Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-13, June.
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