Transversal conics and the existence of limit cycles

2014/10/16 by Giacomini, Héctor, Grau, Maite
#34A34 #34C05 #34C07 #34C25 #37C27 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.4480

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 different 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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