Unpeeling a homoclinic banana in the fitzhugh–nagumo system

Paul Carter, Björn Sandstede

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The FitzHugh–Nagumo equations are known to admit fast traveling pulse solutions with monotone tails. It is also known that this system admits traveling pulses with exponentially decaying oscillatory tails. Upon numerical continuation in parameter space, it has been observed that the oscillations in the tails of the pulses grow into a secondary excursion resembling a second copy of the primary pulse. In this paper, we outline in detail the geometric mechanism responsible for this single-to-double-pulse transition, and we construct the transition analytically using geometric singular perturbation theory and blow-up techniques.

Original languageEnglish (US)
Pages (from-to)236-349
Number of pages114
JournalSIAM Journal on Applied Dynamical Systems
Volume17
Issue number1
DOIs
StatePublished - Jan 1 2018
Externally publishedYes

Keywords

  • Blow-up
  • Canards
  • FitzHugh–Nagumo
  • Geometric singular perturbation theory
  • Traveling waves

Fingerprint Dive into the research topics of 'Unpeeling a homoclinic banana in the fitzhugh–nagumo system'. Together they form a unique fingerprint.

  • Cite this