Travelling waves for diffusive and strongly competitive systems: relative motility and invasion speed

TL;DR

This paper analyzes two-species diffusive competitive systems, revealing that in the case of strong competition, the more diffusive species is the invader, with implications for understanding invasion dynamics.

Contribution

It provides a rigorous analysis of the role of diffusion in invasion speed within strongly competitive Lotka-Volterra systems, highlighting the dominance of the more diffusive species.

Findings

The more diffusive species is the invader in strong competition cases.

Diffusion significantly influences invasion speed and outcome.

Results are specific to homogeneous domains and strong interspecific competition.

Abstract

Our interest here is to find the invader in a two species, diffusive and competitive Lotka-Volterra system in the particular case of travelling wave solutions. We investigate the role of diffusion in homogeneous domains. We might expect a priori two different cases: strong interspecific competition and weak interspecific competition. In this paper, we study the first one and obtain a clear conclusion: the invading species is, up to a fixed multiplicative constant, the more diffusive one.