Limit Cycles of Piecewise-Continuous Differential Systems Formed by Linear and Quadratic Isochronous Centers II

Abstract

We study the crossing periodic orbits and limit cycles of the planar piecewise-continuous differential systems separated by the straight-line [Formula: see text] having in [Formula: see text] the general quadratic isochronous center [Formula: see text], [Formula: see text] after an affine transformation, and in [Formula: see text] an arbitrary quadratic isochronous center except for the quadratic isochronous center [Formula: see text], [Formula: see text] which has been studied in [Ghermoul et al., 2021]. For these piecewise-continuous differential systems the upper bound of crossing limit cycles is 2, and there are specific examples having one crossing limit cycle.