Canard cycles with two breaking parameters

Freddy Dumortier; Robert Roussarie

doi:10.3934/dcds.2007.17.787

Article Contents

2007, Volume 17, Issue 4: 787-806. Doi: 10.3934/dcds.2007.17.787

This issue Previous Article The geometry of mesoscopic phase transition interfaces Next Article Existence, uniqueness, and stability of periodic solutions of an equation of duffing type

Canard cycles with two breaking parameters

Freddy Dumortier^1, and
Robert Roussarie^2,

1.
Universiteit Hasselt, Campus Diepenbeek, Agoralaan–gebouw D, 3590 Diepenbeek
2.
Institut de Mathématique de Bourgogne, U.M.R. 5584 du C.N.R.S., Université de Bourgogne, B.P. 47 870, 21078 Dijon Cedex

Received: June 2006

Revised: September 2006

Published: October 2007

Abstract Related Papers Cited by

Abstract

We consider two-dimensional slow-fast systems with a layer equation exhibiting canard cycles. The canard cycles under consideration contain both a turning point and a fast orbit connecting two jump points. At both the turning point and the connecting fast orbit we suppose the presence of a parameter permitting generic breaking. Such canard cycles depend on two parameters, that we call phase parameters. We study the relaxation oscillations near the canard cycles by means of a map from the plane of phase parameters to the plane of breaking parameters.

Keywords:

Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 34C23, 34C26, 34E15.

Citation:

Article Metrics

HTML views() PDF downloads(181) Cited by(0)

Canard cycles with two breaking parameters

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Canard cycles with two breaking parameters

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content