Sharp Thresholds for Linear Determinacy and Zero Wave Speed in Lotka-Volterra Competition-Diffusion Systems
Abstract
We study two sharp competition thresholds in the Lotka-Volterra competition-diffusion system: the zero-speed threshold for bistable traveling fronts and the linear-determinacy threshold for monostable traveling fronts. Building on our previous results on propagation direction and the classification of traveling waves, we derive explicit Gaussian integral representations of both critical parameters, without involving unknown traveling-wave profiles or speeds. These formulas provide exact characterizations of the optimal competition parameters separating the corresponding propagation regimes. The derivation of these representations was assisted by ChatGPT (OpenAI) Pro, while the underlying theoretical foundations were established in our earlier works.
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BibTeX
@misc{ma2026sharp,
title = {{Sharp Thresholds for Linear Determinacy and Zero Wave Speed in Lotka-Volterra Competition-Diffusion Systems}},
author = {Shizhao Ma and Dongyuan Xiao and Maolin Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16748},
eprint = {2610.16748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16748},
}
RIS
TY - UNPB
TI - Sharp Thresholds for Linear Determinacy and Zero Wave Speed in Lotka-Volterra Competition-Diffusion Systems
AU - Shizhao Ma
AU - Dongyuan Xiao
AU - Maolin Zhou
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16748
UR - https://arxiv.org/abs/2610.16748
AB - We study two sharp competition thresholds in the Lotka-Volterra competition-diffusion system: the zero-speed threshold for bistable traveling fronts and the linear-determinacy threshold for monostable traveling fronts. Building on our previous results on propagation direction and the classification of traveling waves, we derive explicit Gaussian integral representations of both critical parameters, without involving unknown traveling-wave profiles or speeds. These formulas provide exact characterizations of the optimal competition parameters separating the corresponding propagation regimes. The derivation of these representations was assisted by ChatGPT (OpenAI) Pro, while the underlying theoretical foundations were established in our earlier works.
ER -