Competition in periodic media: I -- Existence of pulsating fronts

2016/06/08 by Léo Girardin, Girardin, Léo
Computer Science · Mathematics · Medicine · #35B10 #35B35 #35B40 #35K57 #92D25 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1606.02367

openalex publication_date 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the existence of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. Considering highly competitive systems, a simple "high frequency or small amplitudes" algebraic sufficient condition for the existence of pulsating fronts is stated. This condition is in fact sufficient to guarantee that all periodic coexistence states vanish and become unstable as the competition becomes large enough.

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