Alien limit cycles in Liénard equations
Coll, Bartomeu ![ORCID Identifier](/img/uab/orcid.ico)
(Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Dumortier, Freddy (Universiteit Hasselt(Belgium). Dept. Wiskunde)
Prohens, Rafel ![ORCID Identifier](/img/uab/orcid.ico)
(Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Date: |
2013 |
Abstract: |
This paper aims at providing an example of a family of polynomial Liénard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. The Hamiltonian represents a truncated pendulum of degree 4. In comparison to a former polynomial example, not only the equations are simpler but a lot of tedious calculations can be avoided, making the example also interesting with respect to simplicity in treatment. |
Grants: |
Ministerio de Ciencia e Innovación MTM2011-22751
|
Note: |
Agraïments: The second author thanks the Universitat de les Illes Balears (UIB) for its support as invited professor during the period November to December, 2011. |
Rights: |
Tots els drets reservats. ![](/img/licenses/InC.ico) |
Language: |
Anglès |
Document: |
Article ; recerca ; Versió acceptada per publicar |
Subject: |
Abelian integrals ;
Hamiltonian perturbation ;
Liénard equation ;
Limit cycles ;
Planar vector field ;
Two-saddle cycle ;
Limit cycle ;
Abelian integral |
Published in: |
Journal of differential equations, Vol. 254 (2013) , p. 1582-1600, ISSN 1090-2732 |
DOI: 10.1016/j.jde.2012.11.005
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Record created 2016-05-06, last modified 2022-09-16