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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.
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https://hal.archives-ouvertes.fr/hal-01170521
Contributor : Hector Giacomini <>
Submitted on : Wednesday, July 1, 2015 - 4:27:58 PM
Last modification on : Thursday, December 20, 2018 - 1:27:06 AM

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

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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⟩

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