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http://hdl.handle.net/1942/15848
Title: | Configurations of limit cycles in Lienard equations | Authors: | Coll, B. DUMORTIER, Freddy Prohens, R. |
Issue Date: | 2013 | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 255 (11), p. 4169-4184 | Abstract: | We show that every finite configuration of disjoint simple closed curves in the plane is topologically realizable as the set of limit cy-cles of a polynomial Liénard equation.The related vector field X is Morse–Smale. Moreover it has the minimum numberof singulari-ties required fo rrealizing the configuration in a Liénardequation. We provide an explicit upper bound on the degree of X, which is lower than the results obtained before, obtained in the context of general polynomial vector fields. ©2013ElsevierInc. All rights reserved. | Notes: | Prohens, R (reprint author), Univ Illes Balears, Dept Matemat & Informat, Palma De Mallorca 07122, Illes Balears, Spain. tomeu.coll@uib.cat; freddy.dumortier@uhasselt.be; rafel.prohens@uib.cat | Keywords: | Planar vector field; Lienard equation; Limit cycles configuration; Morse polynomial function | Document URI: | http://hdl.handle.net/1942/15848 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2013.08.004 | ISI #: | 000324960100018 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
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