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http://hdl.handle.net/1942/11743
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DC Field | Value | Language |
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dc.contributor.author | DE MAESSCHALCK, Peter | - |
dc.contributor.author | DUMORTIER, Freddy | - |
dc.date.accessioned | 2011-03-03T08:42:54Z | - |
dc.date.available | NO_RESTRICTION | - |
dc.date.available | 2011-03-03T08:42:54Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | JOURNAL OF DIFFERENTIAL EQUATIONS, 250(4). p. 2162-2176 | - |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.uri | http://hdl.handle.net/1942/11743 | - |
dc.description.abstract | Based on geometric singular perturbation theory we prove the existence of classical Lienard equations of degree 6 having 4 limit cycles. It implies the existence of classical Lienard equations of degree n >= 6, having at least [n-1/2] + 2 limit cycles. This contradicts the conjecture from Lins, de Melo and Pugh formulated in 1976, where an upperbound of [n-1/2] limit cycles was predicted. This paper improves the counterexample from Dumortier, Panazzolo and Roussarie (2007) by supplying one additional limit cycle from degree 7 on, and by finding a counterexample of degree 6. We also give a precise system of degree 6 for which we provide strong numerical evidence that it has at least 3 limit cycles. (c) 2010 Elsevier Inc. All rights reserved. | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.rights | Elsevier Science | - |
dc.subject.other | Slow–fast system; Singular perturbations; Limit cycles; Relaxation oscillation; Classical Liénard equations | - |
dc.subject.other | Slow-fast system; Singular perturbations; Limit cycles; Relaxation oscillation; Classical Lienard equations | - |
dc.title | Classical Lienard equations of degree n >= 6 can have [n-1/2]+2 limit cycles | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 2176 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 2162 | - |
dc.identifier.volume | 250 | - |
local.format.pages | 15 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | [De Maesschalck, P.; Dumortier, F.] Hasselt Univ, B-3590 Diepenbeek, Belgium. | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.bibliographicCitation.oldjcat | A1 | - |
dc.identifier.doi | 10.1016/j.jde.2010.12.003 | - |
dc.identifier.isi | 000286447000014 | - |
item.accessRights | Open Access | - |
item.fullcitation | DE MAESSCHALCK, Peter & DUMORTIER, Freddy (2011) Classical Lienard equations of degree n >= 6 can have [n-1/2]+2 limit cycles. In: JOURNAL OF DIFFERENTIAL EQUATIONS, 250(4). p. 2162-2176. | - |
item.contributor | DE MAESSCHALCK, Peter | - |
item.contributor | DUMORTIER, Freddy | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2012 | - |
crisitem.journal.issn | 0022-0396 | - |
crisitem.journal.eissn | 1090-2732 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
morelc-jde-final.pdf | Peer-reviewed author version | 354.6 kB | Adobe PDF | View/Open |
peter 1.pdf Restricted Access | 224.28 kB | Adobe PDF | View/Open Request a copy |
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