Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11743
Title: Classical Lienard equations of degree n >= 6 can have [n-1/2]+2 limit cycles
Authors: DE MAESSCHALCK, Peter 
DUMORTIER, Freddy 
Issue Date: 2011
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 250(4). p. 2162-2176
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.
Notes: [De Maesschalck, P.; Dumortier, F.] Hasselt Univ, B-3590 Diepenbeek, Belgium.
Keywords: Slow–fast system; Singular perturbations; Limit cycles; Relaxation oscillation; Classical Liénard equations;Slow-fast system; Singular perturbations; Limit cycles; Relaxation oscillation; Classical Lienard equations
Document URI: http://hdl.handle.net/1942/11743
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2010.12.003
ISI #: 000286447000014
Rights: Elsevier Science
Category: A1
Type: Journal Contribution
Validations: ecoom 2012
Appears in Collections:Research publications

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