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http://hdl.handle.net/1942/33877
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DC Field | Value | Language |
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dc.contributor.author | HUZAK, Renato | - |
dc.contributor.author | CRNKOVIC, Vlatko | - |
dc.contributor.author | Vlah, Domagoj | - |
dc.date.accessioned | 2021-04-07T13:03:05Z | - |
dc.date.available | 2021-04-07T13:03:05Z | - |
dc.date.issued | 2021 | - |
dc.date.submitted | 2021-04-06T13:24:33Z | - |
dc.identifier.citation | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501 (2) (Art N° 125212) | - |
dc.identifier.issn | 0022-247X | - |
dc.identifier.uri | http://hdl.handle.net/1942/33877 | - |
dc.description.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. | - |
dc.description.sponsorship | This research was supported by Croatian Science Foundation (HRZZ) Grant PZS-2019-02-3055 from “Research Cooperability” program funded by the European Social Fund | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.rights | 2021 Elsevier Inc. All rights reserved. | - |
dc.subject.other | slow-fast systems | - |
dc.subject.other | slow relation function | - |
dc.subject.other | box dimension | - |
dc.subject.other | fractal zeta function | - |
dc.subject.other | slow-fast Hopf point | - |
dc.title | Fractal dimensions and two-dimensional slow-fast systems | - |
dc.type | Journal Contribution | - |
dc.identifier.issue | 2 | - |
dc.identifier.volume | 501 | - |
local.bibliographicCitation.jcat | A1 | - |
local.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
local.bibliographicCitation.artnr | 125212 | - |
dc.identifier.doi | 10.1016/j.jmaa.2021.125212 | - |
dc.identifier.isi | 000653644000026 | - |
dc.identifier.eissn | 1096-0813 | - |
local.provider.type | - | |
local.uhasselt.uhpub | yes | - |
local.dataset.doi | https://doi.org/10.1016/j.jmaa.2021.125212 | - |
local.uhasselt.international | yes | - |
item.fullcitation | HUZAK, Renato; CRNKOVIC, Vlatko & Vlah, Domagoj (2021) Fractal dimensions and two-dimensional slow-fast systems. In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501 (2) (Art N° 125212). | - |
item.validation | ecoom 2022 | - |
item.accessRights | Open Access | - |
item.fulltext | With Fulltext | - |
item.contributor | HUZAK, Renato | - |
item.contributor | CRNKOVIC, Vlatko | - |
item.contributor | Vlah, Domagoj | - |
crisitem.journal.issn | 0022-247X | - |
crisitem.journal.eissn | 1096-0813 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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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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