Super-linear spreading in local bistable cane toads equations

Bouin, Emeric; Henderson, Christopher

Bouin, Emeric; Henderson, Christopher (2017), Super-linear spreading in local bistable cane toads equations, Nonlinearity, 30, 4, p. n°1356. 10.1088/1361-6544/aa5d65

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01293988

Date

2017

Journal name

Nonlinearity

Volume

Number

Publisher

IOP Publishing

Pages

n°1356

Abstract (EN)

In this paper, we study the influence of an Allee effect on the spreading rate in a local reaction-diffusion-mutation equation modelling the invasion of cane toads in Australia. We are, in particular, concerned with the case when the diffusivity can take unbounded values. We show that the acceleration feature that arises in this model with a Fisher-KPP, or monostable, non-linearity still occurs when this non-linearity is instead bistable, despite the fact that this kills the small populations. This is in stark contrast to the work of Alfaro, Gui-Huan, and Mellet-Roquejoffre-Sire in related models, where the change to a bistable non-linearity prevents acceleration.

Subjects / Keywords

PDE