Traveling Waves in a Three Species Competition-cooperation System

TL;DR

This paper investigates traveling wave solutions in a three-species competition-cooperation system, establishing existence, asymptotics, and uniqueness, with applications to delayed Lotka Volterra models.

Contribution

It introduces a novel approach using monotone iteration with upper and lower solutions from KPP and Lotka Volterra waves, advancing understanding of wave solutions in complex ecological models.

Findings

Existence of traveling waves established via monotone iteration.

Asymptotic behavior and uniqueness of solutions derived.

Applications to delayed Lotka Volterra systems demonstrated.

Abstract

This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves of KPP equation or those of certain Lotka Volterra system. We also derive the asymptotics and uniqueness of the wave solutions. The results are then applied to a Lotka Volterra system with spatially averaged and temporally delayed competition.