PreprintCC BY 4.0arXiv
Spreading speeds for prey-predator systems in a shifting environment: a short proof
Abstract
This note is concerned with the spreading speed of the predator component in a class of prey-predator reaction-diffusion systems with spatiotemporal heterogeneity depending on a moving variable. The main difficulty is that the full system lacks a direct comparison principle. We establish a pointwise estimate showing that the prey density is close to its carrying capacity wherever the predator density is sufficiently small. This allows us to compare solutions of the system with those of scalar Fisher-KPP equations in shifting environments. Consequently, we obtain an explicit formula for the spreading speed of the predator. In particular, for nonmonotone shifting environments, locking and nonlocal pulling phenomena may occur.
Versions
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BibTeX
@misc{jin2026spreading,
title = {{Spreading speeds for prey-predator systems in a shifting environment: a short proof}},
author = {Zhucheng Jin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.14059},
eprint = {2606.14059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14059},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spreading speeds for prey-predator systems in a shifting environment: a short proof
AU - Zhucheng Jin
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2606.14059
UR - https://arxiv.org/abs/2606.14059
AB - This note is concerned with the spreading speed of the predator component in a class of prey-predator reaction-diffusion systems with spatiotemporal heterogeneity depending on a moving variable. The main difficulty is that the full system lacks a direct comparison principle. We establish a pointwise estimate showing that the prey density is close to its carrying capacity wherever the predator density is sufficiently small. This allows us to compare solutions of the system with those of scalar Fisher-KPP equations in shifting environments. Consequently, we obtain an explicit formula for the spreading speed of the predator. In particular, for nonmonotone shifting environments, locking and nonlocal pulling phenomena may occur.
ER -