Non-cooperative Fisher--KPP systems: asymptotic behavior of traveling waves

TL;DR

This paper studies the long-term behavior of traveling wave solutions in non-cooperative reaction-diffusion systems similar to the Fisher--KPP equation, focusing on their asymptotic distributions and modeling complex biological interactions.

Contribution

It analyzes the asymptotic behavior of traveling waves in non-cooperative Fisher--KPP systems, extending understanding beyond scalar equations.

Findings

Traveling wave solutions exist in non-cooperative systems

Asymptotic distributions of these waves are characterized

Models incorporate diffusion, cooperation, and competition mechanisms

Abstract

This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. In a previous paper, we established that these systems admit traveling wave solutions. It is then natural to investigate their asymptotic distributions. This is the main object of this paper. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.