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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/27195

Title: Fractal analysis of canard cycles with two breaking parameters and applications
Authors: Huzak, Renato
Vlah, Domagoj
Issue Date: 2019
Citation: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 18 (2), p. 959-975
Abstract: In previous work [Huzak,2017] we introduced a new box dimension method for computation of the number of limit cycles in planar slow-fast systems, Hausdorff close to balanced canard cycles with one breaking mechanism (the Hopf breaking mechanism or the jump breaking mechanism). This geometric approach consists of a simple iteration method for finding one orbit of the so-called slow relation function and of the calculation of the box dimension of that orbit. Then we read the cyclicity of the balanced canard cycles from the box dimension. The purpose of the present paper is twofold. First, we generalize the box dimension method to canard cycles with two breaking mechanisms. Second, we apply the method from [2017] and our generalized method to a number of interesting examples of canard cycles with one breaking mechanism and with two breaking mechanisms respectively.
Notes: Huzak, R (reprint author), Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. renato.huzak@uhasselt.be; domagoj.vlah@fer.hr
URI: http://hdl.handle.net/1942/27195
Link to publication: http://www.aimsciences.org/article/doi/10.3934/cpaa.2019047
DOI: 10.3934/cpaa.2019047
ISI #: 000446873800020
ISSN: 1534-0392
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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