Limit cycles for discontinuous quadratic differential systems with two zones

In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers x˙=−y+x2, y˙=x+xy and x˙=−y+x2−y2, y˙=x+2xy when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y=0y=0. Comparing the obtained results for the discontinuous with the results for the continuous quadratic polynomial differential systems, this work shows that the discontinuous systems have at least 3 more limit cycles surrounding the origin than the continuous ones.