Bifurcations of multiple relaxation oscillations in polynomial Liénard equations

Peter De Maesschalck, Freddy Dumortier

Type: Article

Publication Date: 2010-11-03

Citations: 14

DOI: https://doi.org/10.1090/s0002-9939-2010-10610-x

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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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Proceedings of the American Mathematical Society - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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+	Canard cycles in the presence of slow dynamics with singularities	2008	Peter De Maesschalck Freddy Dumortier
+	Stable Mappings and Their Singularities	1973	Martin Golubitsky Victor Guillemin