Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11214
Title: DETECTABLE CANARD CYCLES WITH SINGULAR SLOW DYNAMICS OF ANY ORDER AT THE TURNING POINT
Authors: DE MAESSCHALCK, Peter 
DUMORTIER, Freddy 
Issue Date: 2011
Publisher: AMER INST MATHEMATICAL SCIENCES
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 29(1). p. 109-140
Abstract: This paper deals with the study of limit cycles that appear in a class of planar slow-fast systems, near a "canard" limit periodic set of FSTS-type. Limit periodic sets if FSTS-type are closed orbits, composed of a Fast branch, an attracting Slow branch, a Turning point, and a repelling Slow branch. Techniques to bound the number of limit cycles near a FSTS-l.p.s. are based on the study of the so-called slow divergence integral, calculated along the slow branches. In this paper, we extend the technique to the case where the slow dynamics has singulariteis of any (finite) order that accumulate to the turning point, and in which case the slow divergence integral becomes unbounded. Bounds on the number of limit cycles near the FSTS-l.p.s. are derived by examining appropriate derivations of the slow divergence integral.
Notes: [De Maesschalck, Peter; Dumortier, Freddy] Hasselt Univ, B-3590 Diepenbeek, Belgium.
Keywords: slow-fast cycle; turning point; singular perturbations; canards; blow-up; generalized Lienard equation
Document URI: http://hdl.handle.net/1942/11214
ISSN: 1078-0947
e-ISSN: 1553-5231
DOI: 10.3934/dcds.2011.29.109
ISI #: 000281806600007
Category: A1
Type: Journal Contribution
Validations: ecoom 2011
Appears in Collections:Research publications

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