Fast pulses with oscillatory tails in the fitzhugh-nagumo system

Paul Carter, Björn Sandstede

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

Numerical studies indicate that the FitzHugh-Nagumo system exhibits stable traveling pulses with oscillatory tails. In this paper, the existence of such pulses is proved analytically in the singular perturbation limit near parameter values where the FitzHugh-Nagumo system exhibits folds. In addition, the stability of these pulses is investigated numerically, and a mechanism is proposed that explains the transition from single to double pulses that was observed in earlier numerical studies. The existence proof utilizes geometric blow-up techniques combined with the exchange lemma: the main challenge is to understand the passage near two fold points on the slow manifold where normal hyperbolicity fails.

Original languageEnglish (US)
Pages (from-to)3393-3441
Number of pages49
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number5
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

Keywords

  • Blow-up
  • Exchange lemma
  • Fitzhugh-Nagumo
  • Singular perturbation theory
  • Traveling waves

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