Transversal conics and the existence of limit cycles

Giacomini, Héctor; Grau Montaña, Maite

doi:https://doi.org/10.1016/j.jmaa.2015.03.015

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Issue date

2015

Author

Giacomini, Héctor

Grau Montaña, Maite

Suggested citation

Giacomini, Héctor; Grau Montaña, Maite; . (2015) . Transversal conics and the existence of limit cycles. Journal of Mathematical Analysis and Applications, 2015, vol. 428, p. 563-586. https://doi.org/10.1016/j.jmaa.2015.03.015.

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 Poincaré-Bendixson regions by using transversal conics. We present several examples of known systems in the literature showing diferent features

about limit cycles: hyperbolicity, Hopf bifurcation, sky-blue bifurcation, rotated vector fields, . . . for which the obtained Poincaré-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.

URI

http://hdl.handle.net/10459.1/49434

DOI

https://doi.org/10.1016/j.jmaa.2015.03.015

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Journal of Mathematical Analysis and Applications, 2015, vol. 428, p. 563-586

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Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2015