Transversal conics and the existence of limit cycles

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2015Suggested 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.
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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.
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Journal of Mathematical Analysis and Applications, 2015, vol. 428, p. 563-586European research projects
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