Electron. J. Differential Equations, Vol. 2017 (2017), No. 71, pp. 1-7.

Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

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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