Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/10797
Title: Singular perturbations and vanishing passage through a turning point
Authors: DE MAESSCHALCK, Peter 
DUMORTIER, Freddy 
Issue Date: 2010
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 248(9). p. 2294-2328
Abstract: The paper deals with planar slow-fast cycles containing a unique generic turning point. We address the question on how to study canard cycles when the slow dynamics call be singular at the turning point. We more precisely accept a generic saddle-node bifurcation to pass through the turning point. It reveals that in this case the slow divergence integral is no longer the good tool to use, but its derivative with respect to the layer Variable still is. We provide general results as Well as a number of applications. We show how to treat the open problems presented in Artes et al. (2009) [1] and Dumortier and Rousseau (2009) [13], dealing respectively with the graphics DI2a and DF1a from Dumortier et al. (1994) [14]. (C) 2009 Elsevier Inc. All rights reserved.
Notes: [De Maesschalck, P.; Dumortier, F.] Hasselt Univ, B-3590 Diepenbeek, Belgium.
Keywords: Slow-fast cycle; Turning point; Singular perturbations; Canards; Blow-up
Document URI: http://hdl.handle.net/1942/10797
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2009.11.009
ISI #: 000275785100005
Category: A1
Type: Journal Contribution
Validations: ecoom 2011
Appears in Collections:Research publications

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