Zero-Hopf bifurcation in the FitzHugh-Nagumo system

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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2015-11, Vol.38 (17), p.4289-4299
Main Authors: Euzébio, Rodrigo D., Llibre, Jaume, Vidal, Claudio
Format: Article
Language:English
Subjects:
averaging theory
Bifurcations
FitzHugh-Nagumo system
Mathematical analysis
Origins
periodic orbit
zero-Hopf bifurcation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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−. Copyright © 2014 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3365