Huda , Moh Nurul
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Predator Interference-Induced Bistability and Hopf Bifurcation in a Predator–Prey Model with Prey Group Defense and Alternative Food Resmawan, Resmawan; Huda , Moh Nurul; Amanah, Ayu
Indonesian Journal of Mathematics and Applications Vol. 4 No. 2 (2026): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2026.004.02.1

Abstract

This paper investigates an extended predator–prey model incorporating logistic prey growth, prey group defense, alternative food for the predator, and predator interference. The extension is constructed by adding a predator interference term to the denominator of the functional response, so that predation efficiency is affected not only by prey density and alternative food, but also by predator density. The analysis focuses on the existence of equilibrium points, local stability, and bifurcation behavior of the model. The analytical results show that the model admits a predator-free equilibrium, a predator-only equilibrium, and coexistence equilibria. The predator-only equilibrium arises because the predator can persist by utilizing alternative food, even when the main prey becomes extinct. The bifurcation analysis shows the occurrence of transcritical bifurcations at the predator-free and predator-only equilibria, a saddle-node bifurcation at the interior equilibrium, and a Hopf bifurcation at the coexistence equilibrium. Furthermore, variation in the predator interference parameter generates two bistability regimes, namely bistability between the predator-only and predator-free equilibria, and bistability between the predator-free and coexistence equilibria. Numerical simulations support the analytical results and show that the model can exhibit convergence to equilibrium points, structural changes in equilibrium branches, bistability, and a stable limit cycle. These results indicate that the combination of alternative food, prey group defense, and predator interference enriches the dynamics of the predator–prey model. Numerical simulations support the analytical results and show that the model can exhibit convergence to equilibrium points, structural changes in equilibrium branches, bistability, and a numerically observed limit cycle. Ecologically, these dynamics indicate that the long-term outcome of predator–prey interactions may depend on initial population densities and resource conditions, so conservation or management strategies should consider possible shifts among predator extinction, predator persistence supported by alternative food, coexistence, and recurrent population oscillations.