Limit cycles of planar system defined by the sum of two quasi-homogeneous vecter fields

Jianfeng Huang, Haihua Liang

In this paper we consider the limit cycles of the planar system $$\frac{d}{dt}(x,y)={\mathbf{X}}_n+{\mathbf{X}}_m,$$ where ${\mathbf{X}}_n$ and ${\mathbf{X}}_m$ are quasi-homogeneous vector f…