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All Journal Indonesian Journal of Computational and Applied Mathematics
Kasim, Ranan
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Computer Science & IT Engineering Mathematics

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The Occurrence of a Neimark-Sacker Bifurcation on a Discrete-Time Predator-Prey Model Involving Fear Effect and Linear Harvesting Kasim, Ranan; Panigoro, Hasan S.; Rahmi, Emli; Nuha, Agusyarif Rezka; Arsal, Armayani
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 1: February 2025
Publisher : Gammarise Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.64182/indocam.v1i1.5

Abstract

This study investigates the dynamics of a discrete-time predator-prey model incorporating the fear effect and linear harvesting. The model assumes that both prey and predator populations are harvested proportionally to their densities, while the growth rate of the prey population is negatively impacted by predator presence due to fear. The analytical exploration identifies three fixed points: the extinction point, the predator-free equilibrium, and the coexistence equilibrium. Stability analysis and numerical simulations confirm the occurrence of a Neimark-Sacker bifurcation at the interior equilibrium, demonstrating the model's complex dynamical behaviors. The findings provide insights into population sustainability under different harvesting and predation conditions, highlighting how fear and harvesting jointly influence ecosystem stability.
Co-Authors Agusyarif Rezka Nuha Armayani Arsal Hasan S. Panigoro Rahmi, Emli