  The quasi-homogeneous (and in general non-homogeneous) polynomial
differential systems have been studied from many different points of view. In
this paper, Center-focus determination and limit cycles bifurcation for $p:q$
homogeneous weight singular point are investigated. Some prosperities of
Successive function and focus values are discussed, furthermore, the method of
computing focal values is given. As an example, center-focus determination and
limit cycle bifurcation for $2:3$ homogeneous weight singular point are
studied, three or five limit cycles in the neighborhood of origin can be
obtained by different perturbations.
