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http://hdl.handle.net/1942/13216
Title: | Cyclicity of common slow-fast cycles | Authors: | DE MAESSCHALCK, Peter DUMORTIER, Freddy Roussarie, Robert |
Issue Date: | 2011 | Publisher: | ELSEVIER | Source: | INDAGATIONES MATHEMATICAE-NEW SERIES, 22 (3-4), p. 165-206 | Abstract: | We study the limit cycles of planar slow–fast vector fields, appearing near a given slow–fast cycle, formed by an arbitrary sequence of slow parts and fast parts, and where the slow parts can meet the fast parts in a nilpotent contact point of arbitrary order. Using the notion slow divergence integral, we delimit a large subclass of these slow–fast cycles out of which at most one limit cycle can perturb, and a smaller subclass out of which exactly one limit cycle will perturb. Though the focus lies on common slow–fast cycles, i.e. cycles with only attracting or only repelling slow parts, we present results that are valid for more general slow–fast cycles. We also provide examples of attracting common slow–fast cycles out of which more than one limit cycle can perturb, one of which is repelling. | Keywords: | Slow-fast cycle;Cyclicity;Contact point;Singular perturbations;CanardBlow-up;Relaxation oscillation | Document URI: | http://hdl.handle.net/1942/13216 | ISSN: | 0019-3577 | e-ISSN: | 1872-6100 | DOI: | 10.1016/j.indag.2011.09.008 | ISI #: | 000298072500006 | Rights: | 2011 Royal Netherlands Academy of Arts and Sciences. Published by Elsevier B.V. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2013 |
Appears in Collections: | Research publications |
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Cyclicity of common slow-fast cycles.pdf | Published version | 589.18 kB | Adobe PDF | View/Open |
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