Bifurcation of limit cycles and center problem for [formula omitted] homogeneous weight systems

Abstract

The quasi-homogeneous polynomial differential systems have been studied from many different points of view. In this paper, center problem and bifurcation of limit cycles for p:q homogeneous weight systems are studied. Some properties of successive function and focus values are discussed. Furthermore, the method of computing focal values is given. As an example, center problem and bifurcation of limit cycles for 2:3 homogeneous weight system are studied, three or five limit cycles in the neighborhood of origin can be obtained by different perturbations.