New lower bound for the Hilbert number in piecewise quadratic differential systems

Abstract

We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by Hp(n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then Hp(2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center.