Linear spreading speeds from nonlinear resonant interaction

Grégory Faye, Matt Holzer, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on the complex linear dispersion relation at the unstable equilibrium, but rely on the presence of a nonlinear term that facilitates the resonant coupling. We prove that these resonant speeds give the correct invasion speed in a simple example, we show that fronts with speeds slower than the resonant speed are unstable, and corroborate our speed criterion numerically in a variety of model equations, including a nonlocal scalar neural field model.

Original languageEnglish (US)
Pages (from-to)2403-2442
Number of pages40
JournalNonlinearity
Volume30
Issue number6
DOIs
StatePublished - May 10 2017

Bibliographical note

Funding Information:
MH was partially supported by the National Science Foundation through grant NSF-DMS-1516155. AS was partially supported by the National Science Foundation through grant NSF-DMS-1311740 and through a DAAD Fellowship.

Publisher Copyright:
© 2017 IOP Publishing Ltd & London Mathematical Society.

Keywords

  • amplitude equations
  • neural fields
  • resonances
  • spreading speeds
  • traveling fronts

Fingerprint Dive into the research topics of 'Linear spreading speeds from nonlinear resonant interaction'. Together they form a unique fingerprint.

Cite this