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

TL;DR

This paper establishes conditions under which pulsating front solutions exist in space-periodic media for a bistable two-species competition-diffusion system, showing that high competition levels lead to the disappearance of coexistence states.

Contribution

It provides a new algebraic criterion ensuring the existence of pulsating fronts in highly competitive periodic environments.

Findings

High competition causes coexistence states to vanish.

A simple algebraic condition guarantees pulsating front existence.

Coexistence states become unstable with increasing competition.

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.