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http://hdl.handle.net/1942/33002
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DC Field | Value | Language |
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dc.contributor.author | DE MAESSCHALCK, Peter | - |
dc.contributor.author | Doan, Thai Son | - |
dc.contributor.author | WYNEN, Jeroen | - |
dc.date.accessioned | 2020-12-22T10:18:30Z | - |
dc.date.available | 2020-12-22T10:18:30Z | - |
dc.date.issued | 2021 | - |
dc.date.submitted | 2020-12-15T12:30:59Z | - |
dc.identifier.citation | Journal of Dynamics and Differential Equations, 33 (4), p. 2253-2269 | - |
dc.identifier.uri | http://hdl.handle.net/1942/33002 | - |
dc.description.abstract | The presence of slow-fast Hopf (or singular Hopf) points in slow-fast systems in the plane is often deduced from the shape of a vector field brought into normal form. It can however be quite cumbersome to put a system in normal form. In De Maesschalck et al. (Canards from birth to transition, 2020), Wechselberger (Geometric singular perturbation theory beyond the standard form, Springer, New York, 2020) and Jelbart and Wechselberger (Nonlinearity 33(5):2364-2408, 2020) an intrinsic presentation of slow-fast vector fields is initiated, showing hands-on formulas to check for the presence of such singular contact points. We generalize the results in the sense that the criticality of the Hopf bifurcation can be checked with a single formula. We demonstrate the result on a slow-fast system given in non-standard form where slow and fast variables are not separated from each other. The formula is convenient since it does not require any parameterization of the critical curve. | - |
dc.description.sponsorship | This work was supported by the bilateral research cooperation fund of the Research Foundation Flanders (FWO) under Grant No. G0E6618N and the Vietnam National Foundation for Science and Technology (NAFOSTED) under Grant No. FWO.101.2020.01. | - |
dc.language.iso | en | - |
dc.publisher | SPRINGER | - |
dc.rights | Springer Science+Business Media, LLC, part of Springer Nature 2020 | - |
dc.subject.other | Singular bifurcations | - |
dc.subject.other | Slow– | - |
dc.subject.other | fast Hopf bifurcation | - |
dc.subject.other | Criticality | - |
dc.title | Intrinsic Determination of the Criticality of a Slow–Fast Hopf Bifurcation | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 2269 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 2253 | - |
dc.identifier.volume | 33 | - |
local.format.pages | 17 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Wynen, J (corresponding author), Hasselt Univ, Dept Math, Hasselt, Belgium. | - |
dc.description.notes | peter.demaesschalck@uhasselt.be; jeroen.wynen@uhasselt.be | - |
dc.description.other | Wynen, J (corresponding author), Hasselt Univ, Dept Math, Hasselt, Belgium. peter.demaesschalck@uhasselt.be; jeroen.wynen@uhasselt.be | - |
local.publisher.place | ONE NEW YORK PLAZA, SUITE 4600, NEW YORK, NY, UNITED STATES | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1007/s10884-020-09903-x | - |
dc.identifier.isi | WOS:000583460100002 | - |
local.provider.type | wosris | - |
local.uhasselt.uhpub | yes | - |
local.description.affiliation | [De Maesschalck, Peter; Wynen, Jeroen] Hasselt Univ, Dept Math, Hasselt, Belgium. | - |
local.description.affiliation | [Doan, Thai Son] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam. | - |
local.uhasselt.international | yes | - |
item.fullcitation | DE MAESSCHALCK, Peter; Doan, Thai Son & WYNEN, Jeroen (2021) Intrinsic Determination of the Criticality of a Slow–Fast Hopf Bifurcation. In: Journal of Dynamics and Differential Equations, 33 (4), p. 2253-2269. | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2021 | - |
item.contributor | DE MAESSCHALCK, Peter | - |
item.contributor | Doan, Thai Son | - |
item.contributor | WYNEN, Jeroen | - |
item.accessRights | Open Access | - |
crisitem.journal.issn | 1040-7294 | - |
crisitem.journal.eissn | 1572-9222 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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SingularBifurcation_v2a.pdf | Peer-reviewed author version | 262.53 kB | Adobe PDF | View/Open |
s10884-020-09903-x.pdf Restricted Access | Published version | 269.52 kB | Adobe PDF | View/Open Request a copy |
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