Sharp Thresholds for Linear Determinacy and Zero Wave Speed in Lotka-Volterra Competition-Diffusion Systems
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Ma, Shizhao, Xiao, Dongyuan, Zhou, Maolin
Institutions: Shanghai Jiao Tong University, Nankai University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221828312