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Title: | Fractal dimensions and two-dimensional slow-fast systems | Authors: | HUZAK, Renato CRNKOVIC, Vlatko Vlah, Domagoj |
Issue Date: | 2021 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501 (2) (Art N° 125212) | Abstract: | In our paper we present a fractal analysis of canard cycles and slow-fast Hopf points in 2-dimensional singular perturbation problems under very general conditions. Our focus is on the orientable case (e.g. R 2) and the non-orientable case (e.g. the Möbius band). Given a slow-fast system, we generate a sequence of real numbers using the so-called slow relation function and compute a fractal dimension of that sequence. Then the value of the fractal dimension enables us to determine the cyclicity and bifurcations of canard cycles in the slow-fast system. We compute the fractal dimension of a slow-fast Hopf point depending on its codimension. Our focus is on the box dimension, one-sided dimensions and the fractal zeta-function. We also find explicit fractal formulas of Cahen-type for the computation of the above fractal dimensions and use them to detect numerically the number of canard limit cycles. | Keywords: | slow-fast systems;slow relation function;box dimension;fractal zeta function;slow-fast Hopf point | Document URI: | http://hdl.handle.net/1942/33877 | ISSN: | 0022-247X | e-ISSN: | 1096-0813 | DOI: | https://doi.org/10.1016/j.jmaa.2021.125212 | ISI #: | 000653644000026 | Datasets of the publication: | https://doi.org/10.1016/j.jmaa.2021.125212 | Rights: | 2021 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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FractalDimensions.pdf | Peer-reviewed author version | 741.63 kB | Adobe PDF | View/Open |
Fractal dimensions and two-dimensional slow-fast systems.pdf Restricted Access | Published version | 921.09 kB | Adobe PDF | View/Open Request a copy |
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