Super-linear spreading in local bistable cane toads equations

Emeric Bouin (1) , Christopher Henderson (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 NUMED - Numerical Medicine
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Domaines: Equations aux dérivées partielles [math.AP]

Emeric Bouin, Christopher Henderson. Super-linear spreading in local bistable cane toads equations. 2016. ⟨hal-01293988⟩