Ahmed Bendjeddou, Rachid Cheurfa
Abstract:
In the work by Gine and Grau [11], a planar differential
system of degree nine admitting a nested configuration formed by
an algebraic and a non-algebraic limit cycles explicitly given was presented.
As an improvement, we obtain by a new method a similar result for a family of
quintic polynomial differential systems.
Submitted January 2, 2017. Published March 14, 2017.
Math Subject Classifications: 34C29, 34C25.
Key Words: Non-algebraic limit cycle; invariant curve; Poincare return-map;
first integral; Riccati equation.
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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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