Please use this identifier to cite or link to this item: 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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