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http://hdl.handle.net/1942/11566
Title: | Slow-fast Bogdanov-Takens bifurcations | Authors: | DE MAESSCHALCK, Peter DUMORTIER, Freddy |
Issue Date: | 2011 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 250(2). p. 1000-1025 | Abstract: | In this paper we study perturbations from planar vector fields having a line of zeros and representing a singular limit of Bogdanov-Takens (BT) bifurcations. We introduce, among other precise definitions, the notion of slow-fast BT-bifurcation and we provide a complete study of the bifurcation diagram and the related phase portraits. Based on geometric singular perturbation theory, including blow-up, we get results that are valid on a uniform neighborhood both in parameter space and in the phase plane. (C) 2010 Elsevier Inc. All rights reserved. | Notes: | [De Maesschalck, P.; Dumortier, F.] Hasselt Univ, B-3590 Diepenbeek, Belgium. | Keywords: | Singular perturbations; Bogdanov-Takens bifurcation; Limit cycles | Document URI: | http://hdl.handle.net/1942/11566 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2010.07.022 | ISI #: | 000285490300015 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2012 |
Appears in Collections: | Research publications |
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