Resonance in excitable systems under step-function forcing II. Subharmonic solutions and persistence

Min Xie, Hans G. Othmer, Masaji Watanabe

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In an earlier paper (Othmer and Watanabe, 1994) we studied the existence and stability of harmonic solutions in a Fitzhugh-Nagumo type model under step-function forcing. In this paper we study subharmonic solutions, and show that a number of phenomena arise which do not occur in invertible circle maps. In particular, we show that the rotation number may be non-monotonic or discontinuous in one-parameter families, and that stable periodic solutions with different rotation numbers coexist on open sets in parameter space. The latter result shows how an experimental observation first due to Mines (1913) can be understood in the context of a flow. We also show that the 'stable' results for the singular system persist in the non-singular system, in a sense made precise later.

Original languageEnglish
Pages (from-to)75-110
Number of pages36
JournalPhysica D: Nonlinear Phenomena
Volume98
Issue number1
Publication statusPublished - 1996

Fingerprint

Subharmonic Solutions
Excitable Systems
step functions
Rotation number
Step function
Persistence
Forcing
Circle Map
FitzHugh-Nagumo
Singular Systems
Open set
Invertible
Parameter Space
Periodic Solution
Harmonic
harmonics
Model
Context
Family
Observation

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Resonance in excitable systems under step-function forcing II. Subharmonic solutions and persistence. / Xie, Min; Othmer, Hans G.; Watanabe, Masaji.

In: Physica D: Nonlinear Phenomena, Vol. 98, No. 1, 1996, p. 75-110.

Research output: Contribution to journalArticle

Xie, Min ; Othmer, Hans G. ; Watanabe, Masaji. / Resonance in excitable systems under step-function forcing II. Subharmonic solutions and persistence. In: Physica D: Nonlinear Phenomena. 1996 ; Vol. 98, No. 1. pp. 75-110.
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