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|Title:||Numerical continuation techniques for planar slow-fast systems||Authors:||De Maesschalck, P.
|Issue Date:||2013||Source:||SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 12(3). p. 1159-1180||Abstract:||Continuation techniques have been known to successfully describe bifurcation diagrams appearing in slow-fast systems with more than one slow variable. In this paper we investigate the usefulness of numerical continuation techniques dealing with some solved and some open problems in the study of planar singular perturbations. More precisely, we first verify known theoretical results (thereby showing the reliability of the numerical tools) on the appearance of multiple limit cycles of relaxation-oscillation type and on the existence of multiple critical periods in well-chosen annuli of slow-fast periodic orbits in the plane. We then apply the technique to study a notion of maximal canard, in the sense of maximal period.||Keywords:||singular perturbations; Liénard systems; canards; critical periods; numerical continuation||Document URI:||http://hdl.handle.net/1942/13228||ISSN:||1536-0040||e-ISSN:||****-****||DOI:||10.1137/120877386||ISI #:||000325009700001||Category:||A1||Type:||Journal Contribution||Validations:||ecoom 2014|
|Appears in Collections:||Research publications|
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