Dynamics of a Harvested Predator-Prey Model with a Generalized Holling Type~III Response Capturing Group Defense
Abstract
We investigate a predator-prey model with constant prey harvesting and a generalized Holling type III functional response, focusing on the biological and dynamical consequences of allowing the parameter b to be negative. In this regime, predation efficiency declines at high prey densities, potentially reflecting group defense. This change permits an additional coexistence equilibrium and introduces new bifurcation mechanisms affecting population persistence. We establish the existence of a codimension-three Bogdanov--Takens bifurcation, derive a codimension-three nilpotent-saddle unfolding, and investigate a codimension-two generalized Hopf bifurcation and the emergence of multiple limit cycles. Our analysis show that moderate harvesting weakens the protection conferred by high prey abundance; excessive harvesting leaves too few prey to sustain predator growth; and low harvesting preserves strong group defense, requiring high predator density for population persistence.
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BibTeX
@misc{khateeb2026dynamics,
title = {{Dynamics of a Harvested Predator-Prey Model with a Generalized Holling Type~III Response Capturing Group Defense}},
author = {Wael El Khateeb and Farjana Akter and Chanaka Kottegoda and Muner Mustafa Abou Hasan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32306},
eprint = {2610.32306},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32306},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamics of a Harvested Predator-Prey Model with a Generalized Holling Type~III Response Capturing Group Defense
AU - Wael El Khateeb
AU - Farjana Akter
AU - Chanaka Kottegoda
AU - Muner Mustafa Abou Hasan
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32306
UR - https://arxiv.org/abs/2610.32306
AB - We investigate a predator-prey model with constant prey harvesting and a generalized Holling type III functional response, focusing on the biological and dynamical consequences of allowing the parameter b to be negative. In this regime, predation efficiency declines at high prey densities, potentially reflecting group defense. This change permits an additional coexistence equilibrium and introduces new bifurcation mechanisms affecting population persistence. We establish the existence of a codimension-three Bogdanov--Takens bifurcation, derive a codimension-three nilpotent-saddle unfolding, and investigate a codimension-two generalized Hopf bifurcation and the emergence of multiple limit cycles. Our analysis show that moderate harvesting weakens the protection conferred by high prey abundance; excessive harvesting leaves too few prey to sustain predator growth; and low harvesting preserves strong group defense, requiring high predator density for population persistence.
ER -