Super-linear spreading in local bistable cane toads equations

Emeric Bouin, Christopher Henderson

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we study the influence of an Allee effect on the spreading rate in a local reaction-diffusion-mutation equation modeling 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, nonlinearity still occurs when this nonlinearity 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 nonlinearity prevents acceleration.

Original languageEnglish (US)
Pages (from-to)1356-1375
Number of pages20
JournalNonlinearity
Volume30
Issue number4
DOIs
StatePublished - Feb 21 2017
Externally publishedYes

Keywords

  • acceleration
  • Allee effect
  • bistable reaction
  • cane toads equation
  • reaction diffusion equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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