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arXiv · 2608.24253

Critical Three-Species Competition-Diffusion: Traveling-Wave Rigidity and the Fastest-Species Selection

Haozhe Shu·Dongyuan Xiao
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Abstract

We study the rigidity of traveling waves and long-time species selection in a one-dimensional critical three-species competition-diffusion system. We establish several rigidity results for traveling waves connecting distinct equilibria on the critical simplex. In the case where one species has a strictly larger Fisher-KPP spreading speed than the other two, an entropy method, combined with Gagliardo-Nirenberg and Nash inequalities yieldsuniform extinction of the slower species and convergence to the fastest-species equilibrium throughout every cone with speed below its KPP speed.

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Haozhe Shu, Dongyuan Xiao. 2026-08-25. Critical Three-Species Competition-Diffusion: Traveling-Wave Rigidity and the Fastest-Species Selection. https://arxiv.org/abs/2608.24253

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