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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2015

Transversal conics and the existence of limit cycles

Résumé

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.

Dates et versions

hal-01170521 , version 1 (01-07-2015)

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