Predator self limitation controls pattern formation in a predator prey system with additional food: a Turing Hopf analysis
Abstract
Supplying a released predator with additional, non reproducing food is a standard lever in augmentative biological control, with a known drawback with nothing limiting the predators own numbers, the extra food lets its population grow without bound. Competition among the predators supplies the missing brake. Howthis self limitation reshapes the spatial arrangement of the two species has not been asked. We address it with a reaction diffusion model of a logistically growing prey and a predator feeding through a Holling type II response that also draws on additional food , the predators competing among themselves at strength. In the well mixed setting we locate the Hopf bifurcation of the coexistence state exactly and show the cycle born there is stable, so weak competition gives boom bust oscillations, not runaway growth. Allowing movement, we obtain the diffusion driven Turing threshold at which the uniform state breaks into stationary patches of high and low density, and find the uniform oscillation stable as it appears. With prey mobility and competition strength as control parameters, the pattern forming and oscillatory instabilities meet at a single point, where we compute the dynamics. Simulations confirm the sequence weak competition gives a wholefield oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time. Predator self competition therefore sets the spatial structure of the community, which is what matters when additional food is used to steer a control agent in the field.
Related
- Cascading fishery collapse associated with thermal habitat degradation, marine heatwaves, and predator influx
- Potential of Tecoma stans as an Insectary Plant for the Mirid Predator Tytthus chinensis (Hemiptera: Miridae): Effects on Longevity and Reproductive Development
- Hide and seek in a rainforest canopy : when a fruit-eating carnivore (almost) met its top predator carnivore
- Dynamics and optimal harvesting of a fractional predator–prey system with fear and anti-predator mechanisms
- Behavioural strategy and predator control: a coupled evolutionary predator-prey model for kiwi conservation in New Zealand
BibTeX
@misc{hazra2026predator,
title = {{Predator self limitation controls pattern formation in a predator prey system with additional food: a Turing Hopf analysis}},
author = {Anushree Hazra and Aniket Banerjee and Debaldev Jana},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29052},
eprint = {2609.29052},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29052},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Predator self limitation controls pattern formation in a predator prey system with additional food: a Turing Hopf analysis
AU - Anushree Hazra
AU - Aniket Banerjee
AU - Debaldev Jana
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.29052
UR - https://arxiv.org/abs/2609.29052
AB - Supplying a released predator with additional, non reproducing food is a standard lever in augmentative biological control, with a known drawback with nothing limiting the predators own numbers, the extra food lets its population grow without bound. Competition among the predators supplies the missing brake. Howthis self limitation reshapes the spatial arrangement of the two species has not been asked. We address it with a reaction diffusion model of a logistically growing prey and a predator feeding through a Holling type II response that also draws on additional food , the predators competing among themselves at strength. In the well mixed setting we locate the Hopf bifurcation of the coexistence state exactly and show the cycle born there is stable, so weak competition gives boom bust oscillations, not runaway growth. Allowing movement, we obtain the diffusion driven Turing threshold at which the uniform state breaks into stationary patches of high and low density, and find the uniform oscillation stable as it appears. With prey mobility and competition strength as control parameters, the pattern forming and oscillatory instabilities meet at a single point, where we compute the dynamics. Simulations confirm the sequence weak competition gives a wholefield oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time. Predator self competition therefore sets the spatial structure of the community, which is what matters when additional food is used to steer a control agent in the field.
ER -