Stacked invasion waves in a competition-diffusion model with three species

TL;DR

This paper analyzes the spreading dynamics of a three-species competition-diffusion system using Hamilton-Jacobi methods, providing the first theoretical characterization of invasion waves in such complex multi-species models.

Contribution

It introduces a novel application of Hamilton-Jacobi techniques to derive sharp estimates and explicit formulas for spreading speeds in a three-species competition system.

Findings

Derived upper and lower bounds for spreading speeds.

Established explicit formulas for invasion wave speeds.

First theoretical analysis of three-species competition in unbounded domains.

Abstract

We investigate the spreading properties of a three-species competition-diffusion system, which is non-cooperative. We apply the Hamilton-Jacobi approach, due to Freidlin, Evans and Souganidis, to establish upper and lower estimates of spreading speed of the slowest species, in terms of the spreading speed of two faster species, and show that the estimates are sharp in some situations. The spreading speed will first be characterized as the free boundary point of the viscosity solution for certain variational inequality cast in the space of speeds. Its exact formulas will then be derived by solving the variational inequality explicitly. To the best of our knowledge, this is the first theoretical result on three-species competition system in unbounded domains.