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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/dataset: | 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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