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

Dian Savitri, Agus Suryanto, Wuryansari Muharini Kusumawinahyu and Abadi
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Dian Savitri: Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, 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

Mathematics, 2020, vol. 8, issue 5, 1-16

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.

Keywords: modified Leslie–Gower; two predator–one prey interaction; stability analysis; Lyapunov function; saddle-node bifurcation; transcritical bifurcation; bi-stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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