Stability for a family of planar systems with nilpotent critical points

Ziwei Zhuang, Changjian Liu

Consider a family of planar polynomial systems $\dot{x}=y^{2l-1}-x^{2k+1},\dot{y}=-x+m{y}^{2s+1},$ where $l,k,s\in {\mathbb{N}}^{\ast },$ $2\le l\le 2s$ and $m\in \mathbb{R}.$ We study…