Spreading--vanishing dynamics and speed selection in a free-boundary competition model under a shifting climate
Abstract
We study a free boundary problem for a diffusive Lotka--Volterra competition system describing the invasion of a new species into the habitat of a native competitor, where habitat suitability shifts from unfavourable to favourable at a constant speed c>0 due to climate change. Only the invader is affected by the shifting environment and only its range is governed by a Stefan-type free boundary, while the native species occupies the whole half line. We work throughout in the weak competition regime, in which the two species may coexist. We prove a spreading--vanishing dichotomy: either the invader spreads and the pair converges to the coexistence steady state (u*,v*), or the invader vanishes and the native species recovers its carrying capacity. In the vanishing case we obtain the explicit bound limt→∞h(t)≤π/2√(d1c2/(a1c2−a2c1)), and we give criteria guaranteeing each alternative. When spreading occurs, we determine the exact asymptotic spreading speed: limt→∞h(t)/t=min{c,c0}, where c0 is the spreading speed of the corresponding homogeneous weak competition system. In particular the invasion is slowed down both by the competitor and by the climate shift, and the slower of the two mechanisms is the one that determines the speed. Numerical simulations illustrate the results.
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BibTeX
@misc{dinh2026spreadingvanishing,
title = {{Spreading--vanishing dynamics and speed selection in a free-boundary competition model under a shifting climate}},
author = {Phuoc Vinh Dinh and Phuong Le and Tien Dung Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.14679},
eprint = {2609.14679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14679},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spreading--vanishing dynamics and speed selection in a free-boundary competition model under a shifting climate
AU - Phuoc Vinh Dinh
AU - Phuong Le
AU - Tien Dung Nguyen
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.14679
UR - https://arxiv.org/abs/2609.14679
AB - We study a free boundary problem for a diffusive Lotka--Volterra competition system describing the invasion of a new species into the habitat of a native competitor, where habitat suitability shifts from unfavourable to favourable at a constant speed c>0 due to climate change. Only the invader is affected by the shifting environment and only its range is governed by a Stefan-type free boundary, while the native species occupies the whole half line. We work throughout in the weak competition regime, in which the two species may coexist. We prove a spreading--vanishing dichotomy: either the invader spreads and the pair converges to the coexistence steady state (u^*,v^*), or the invader vanishes and the native species recovers its carrying capacity. In the vanishing case we obtain the explicit bound lim_t→∞h(t)≤π/2√(d_1c_2/(a_1c_2−a_2c_1)), and we give criteria guaranteeing each alternative. When spreading occurs, we determine the exact asymptotic spreading speed: lim_t→∞h(t)/t=min{c,c_0}, where c_0 is the spreading speed of the corresponding homogeneous weak competition system. In particular the invasion is slowed down both by the competitor and by the climate shift, and the slower of the two mechanisms is the one that determines the speed. Numerical simulations illustrate the results.
ER -