Limit Cycles Bifurcating from Planar Polynomial Quasi-Homogeneous Centers of Weight-Degree 3 with Nonsmooth Perturbations

In this paper, we estimate the number of limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3, when they are perturbed inside the class of piecewise smooth polynomial systems of degree n. By using the first-order averaging method, we give the upper and lower bounds on the maximal number of limit cycles which can bifurcate from the period annuluses. Our results indicate that the nonsmooth systems can have more limit cycles than the smooth ones.