Zero-Hopf bifurcation in the FitzHugh-Nagumo system

Rodrigo D. Euzébio, Jaume Llibre, Claudio Vidal

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

Copyright © 2014 John Wiley & Sons, Ltd. We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+, and P- in the FitzHugh-Nagumo system. We find two two-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families, we prove the existence of a periodic orbit bifurcating from the zero-Hopf equilibrium point O. We prove that there exist three two-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at P+ and at P- is a zero-Hopf equilibrium point. For one of these families, we prove the existence of one, two, or three periodic orbits starting at P+ and P-.
Original languageEnglish
Pages (from-to)4289-4299
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number17
DOIs
Publication statusPublished - 30 Nov 2015

Keywords

  • averaging theory
  • FitzHugh-Nagumo system
  • periodic orbit
  • zero-Hopf bifurcation

Fingerprint Dive into the research topics of 'Zero-Hopf bifurcation in the FitzHugh-Nagumo system'. Together they form a unique fingerprint.

  • Cite this