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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 | Source: | 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 | Keywords: | box dimension; canard cycles; singular perturbation theory; slow divergence integral; Tricot method | Document URI: | http://hdl.handle.net/1942/27195 | Link to publication/dataset: | http://www.aimsciences.org/article/doi/10.3934/cpaa.2019047 | ISSN: | 1534-0392 | e-ISSN: | 1553-5258 | DOI: | 10.3934/cpaa.2019047 | ISI #: | 000446873800020 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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FractalAnalysisCanard .pdf | Peer-reviewed author version | 617.27 kB | Adobe PDF | View/Open |
Huzak.pdf Restricted Access | Published version | 608.78 kB | Adobe PDF | View/Open Request a copy |
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