Existence of Traveling Waves for a Diffusive Nicholson Equation with Harvesting
Abstract
We prove the existence of traveling wave solutions for a diffusive Nicholson model with a delayed linear harvesting term and two delayed-response channels. Our approach combines monotone heteroclinic connections of the associated scalar delay equation with the large-speed traveling-wave theorem of Faria, Huang and Wu. For 0<σ<r, we use a previous upper- and lower-solution construction under an explicit parameter condition. For 0<r≤σ, we establish a new monotone heteroclinic connection. To fit the abstract framework, we embed the scalar equation into an auxiliary two-dimensional reaction--diffusion system and prove that every relevant traveling wave lies on the invariant diagonal. We then determine an explicit parameter region in which the required spectral hypotheses hold. Consequently, the original diffusive Nicholson equation admits traveling waves connecting the trivial and positive equilibria for all sufficiently large wave speeds.
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BibTeX
@misc{gomez2026existence,
title = {{Existence of Traveling Waves for a Diffusive Nicholson Equation with Harvesting}},
author = {Adrián Gómez and Helí Elorreaga and Cesar Guayasamin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21166},
eprint = {2609.21166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21166},
}
RIS
TY - UNPB
TI - Existence of Traveling Waves for a Diffusive Nicholson Equation with Harvesting
AU - Adrián Gómez
AU - Helí Elorreaga
AU - Cesar Guayasamin
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21166
UR - https://arxiv.org/abs/2609.21166
AB - We prove the existence of traveling wave solutions for a diffusive Nicholson model with a delayed linear harvesting term and two delayed-response channels. Our approach combines monotone heteroclinic connections of the associated scalar delay equation with the large-speed traveling-wave theorem of Faria, Huang and Wu. For 0<σ<r, we use a previous upper- and lower-solution construction under an explicit parameter condition. For 0<r≤σ, we establish a new monotone heteroclinic connection. To fit the abstract framework, we embed the scalar equation into an auxiliary two-dimensional reaction--diffusion system and prove that every relevant traveling wave lies on the invariant diagonal. We then determine an explicit parameter region in which the required spectral hypotheses hold. Consequently, the original diffusive Nicholson equation admits traveling waves connecting the trivial and positive equilibria for all sufficiently large wave speeds.
ER -