Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/4045
Title: Bifurcation of relaxation oscillations in dimension two
Authors: DUMORTIER, Freddy 
Roussarie, Robert
Issue Date: 2007
Publisher: AMER INST MATHEMATICAL SCIENCES
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 19(4). p. 631-674
Abstract: The paper deals with the bifurication of relaxation oscillations in two dimensional slow-fast systems. The most generic case is studied by means of gemoetric singular perturbation theory, using blow up at contact points. It reveals that the bifurication goes through a continuum of transient canard oscillations, controlled by the slow divergence integral alonng the critical curve. The theory is applied to polynomial Lienard equations, showing that the cyclicity near a generic coallescence of two relaxation oscillations does not need to be limited to two, but can be arbitarily high.
Notes: Univ Hasselt, B-3590 Diepenbeek, Belgium. Univ Bourgogne, Inst Math Bourgogne, UMR 5584, CNRS, F-21078 Dijon, France.DUMORTIER, F, Univ Hasselt, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.roussari@u-bourgogne.fr
Keywords: slow-fast system; bifurcation; relaxation oscillation; canard cycle; Lienard equation
Document URI: http://hdl.handle.net/1942/4045
Link to publication: http://aimsciences.org/journals/pdfs.jsp?paperID=2821&mode=abstract
ISSN: 1078-0947
e-ISSN: 1553-5231
ISI #: 000249791100002
Category: A1
Type: Journal Contribution
Validations: ecoom 2008
Appears in Collections:Research publications

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