Heterogeneity and strong competition in ecology

TL;DR

This paper investigates a competition-diffusion model in ecology, deriving a Stefan type evolution equation through homogenization and strong competition limits, and explores how oscillations affect species invasion via numerical simulations.

Contribution

It introduces a novel combined homogenization and strong competition limit analysis leading to a Stefan type equation in ecological modeling.

Findings

Oscillations hinder species invasion in numerical simulations.

Derived effective coefficients in the Stefan type evolution equation.

Homogenization captures heterogeneity effects in competition models.

Abstract

We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical simulations in one and two spatial dimensions that suggest that oscillations are detrimental to invasion behaviour of the species.