Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems

TL;DR

This paper extends the analysis of spreading speeds and traveling waves to non-cooperative reaction-diffusion systems, providing a framework for understanding their dynamics and applying it to ecological models.

Contribution

It establishes the spreading speed for a broad class of non-cooperative systems and characterizes it via traveling wave solutions, a novel approach compared to cooperative systems.

Findings

Spreading speed characterized as the slowest traveling wave speed.

Application to a model of ungulates and grass interactions.

Framework applicable to various non-cooperative systems.

Abstract

Much has been studied on the spreading speed and traveling wave solutions for cooperative reaction-diffusion systems. In this paper, we shall establish the spreading speed for a large class of non-cooperative reaction-diffusion systems and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. As an application, our results are applied to a partially cooperative system describing interactions between ungulates and grass.