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arXiv · 1211.3858

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

Benoit Sarels
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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.

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Benoit Sarels. 2012-11-16. Generalized traveling wave in heterogeneous media: Allee effect can inhibit invasion. https://arxiv.org/abs/1211.3858

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