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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