Alien limit cycles in Liénard equations

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 pendul...

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Bibliographic Details
Published in:Journal of Differential Equations 2013-02, Vol.254 (3), p.1582-1600
Main Authors: Coll, B., Dumortier, F., Prohens, R.
Format: Article
Language:English
Subjects:
2-Saddle cycle
Abelian integral
Hamiltonian perturbation
Limit cycle
Liénard equation
Planar vector field
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.11.005