Bifurkasi pada Model Predator-Prey Diskret dengan Fungsi Respon Ratio-Depedent dan  Pemanenan

Agus Suryanto; Vira Hari Krisnawati; Sri Puji Lestari; Denis Andre Matatula; Mohammad Fahrurrozy

doi:10.12962/limits.v22i2.3450

Authors

Agus Suryanto Department of Mathematics, University of Brawijaya
Vira Hari Krisnawati Department of Mathematics, Universitas Brawijaya Malang
Sri Puji Lestari Department of Mathematics, Universitas Brawijaya Malang
Denis Andre Matatula Department of Mathematics, Universitas Brawijaya Malang
Mohammad Fahrurrozy Department of Mathematics, Universitas Brawijaya Malang

DOI:

https://doi.org/10.12962/limits.v22i2.3450

Keywords:

stability analysis, period-doubling bifurcation, Neimark-Sacker bifurcation

Abstract

This article discusses a predator-prey model with a ratio-dependent functional response and harvesting in both populations. The differential equation of predator-prey model is discretized using the Euler method. The dynamics of the obtained discrete time model are investigated by determining the fixed points as well as their stability properties, and bifurcation analysis. Bifurcation analysis shows that the discrete time model can experience bifurcation, both period-doubling bifurcation and Neimark-Sacker bifurcation, when the value of time-integration step passes a critical value. The analysis results have been confirmed by our numerical simulation results presented at the end of this article.

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