Electron. J. Diff. Equ., Vol. 2011 (2011), No. 15, pp. 1-12.

Cubic and quartic planar differential systems with exact algebraic limit cycles

Ahmed Bendjeddou, Rachid Cheurfa

Abstract:
We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur.

Submitted April 28, 2010. Published January 26, 2011.
Math Subject Classifications: 34C05, 34A34, 34C25.
Key Words: Polynomial system; invariant curve; algebraic curve; limit cycle; Hilbert 16th problem.

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Ahmed Bendjeddou
Département de Mathématiques
Faculté des Sciences, Université de Sétif
19000 Sétif, Algérie
email: Bendjeddou@univ-setif.dz
Rachid Cheurfa
Département de Mathématiques
Faculté des Sciences, Université de Sétif
19000 Sétif, Algérie
email: rcheurfa@yahoo.fr

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