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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bifurcations of multiple relaxation oscillations in polynomial Liénard equations


Authors: P. De Maesschalck and F. Dumortier
Journal: Proc. Amer. Math. Soc. 139 (2011), 2073-2085
MSC (2010): Primary 37G15, 34E17; Secondary 34C07, 34C26
Published electronically: November 3, 2010
MathSciNet review: 2775385
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Abstract: In this paper, we prove the presence of limit cycles of given multiplicity, together with a complete unfolding, in families of (singularly perturbed) polynomial Liénard equations. The obtained limit cycles are relaxation oscillations. Both classical Liénard equations and generalized Liénard equations are treated.


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Additional Information

P. De Maesschalck
Affiliation: Hasselt University, Campus Diepenbeek, Agoralaan gebouw D, B-3590 Diepenbeek, Belgium
Email: peter.demaesschalck@uhasselt.be

F. Dumortier
Affiliation: Hasselt University, Campus Diepenbeek, Agoralaan gebouw D, B-3590 Diepenbeek, Belgium
Email: freddy.dumortier@uhasselt.be

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10610-X
PII: S 0002-9939(2010)10610-X
Keywords: Slow-fast system, singular perturbations, limit cycles, relaxation oscillation, polynomial Liénard equations, elementary catastrophy
Received by editor(s): March 24, 2010
Received by editor(s) in revised form: May 31, 2010
Published electronically: November 3, 2010
Additional Notes: The first author was supported by the Research Foundation Flanders.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.