Bifurcation of Limit Cycles in a Particular Class of Quadratic Systems with Two Centers

Within the class of quadratic perturbations we show analytically or numerically how many limit cycles can be bifurcated at first order out of the periodic orbits nested around the centre point in (0, 0) or nested around the centre point in (0, 1/n) of the quadratic system = −y + ny2, = x − xy with 0 < n < 1.