Generalized traveling wave in heterogeneous media: Allee effect can inhibit invasion

TL;DR

This paper investigates how the Allee effect influences invasion dynamics in heterogeneous media using a reaction-diffusion model, introducing a generalized traveling wave concept and revealing conditions for invasion pinning.

Contribution

It introduces a generalized traveling wave framework for reaction-diffusion models with Allee effect and heterogeneity, providing new insights into invasion pinning phenomena.

Findings

Allee effect can inhibit invasion in heterogeneous media.

A new definition of generalized traveling wave is proposed.

Conditions for invasion pinning are established.

Abstract

In this paper, we study a simple one-dimensional model of reaction-diffusion with bistable non-linearity and in heterogeneous media. The bistable term accounts for the so-called Allee effect, and the heterogeneity in the media is localized. We recall the definition of a transition wave used in similar situations by well-known authors, and propose an alternative definition for discussion. We call it generalized traveling wave. As a consequence, we give new results of pinning in such media, due to Allee effect.