Transversal conics and the existence of limit cycles

Abstract : This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincar\'e--Bendixson regions by using transversal conics. We present several examples of known systems in the literature showing different features about limit cycles: hyperbolicity, Hopf bifurcation, sky-blue bifurcation, rotated vector fields, \ldots for which the obtained Poincar\'e--Bendixson region allows to locate the limit cycles. Our method gives bounds for the bifurcation values of parametrical families of planar vector fields and intervals of existence of limit cycles.
Type de document :
Article dans une revue
Journal of Mathematical Analysis and Applications, Elsevier, 2015, 428 (1), pp.563-586
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01170521
Contributeur : Hector Giacomini <>
Soumis le : mercredi 1 juillet 2015 - 16:27:58
Dernière modification le : jeudi 20 décembre 2018 - 01:27:06

Lien texte intégral

Identifiants

  • HAL Id : hal-01170521, version 1
  • ARXIV : 1410.4480

Collections

Citation

Héctor Giacomini, Maite Grau. Transversal conics and the existence of limit cycles. Journal of Mathematical Analysis and Applications, Elsevier, 2015, 428 (1), pp.563-586. 〈hal-01170521〉

Partager

Métriques

Consultations de la notice

86