The problem of determining the basin of attraction of equilibrium points is of great importance for applications of stability theory. In this article, we address the global asymptotic stability problem of an equilibrium point of an ordinary differential equation on the plane. More precisely, we study equilibrium points of Kukles systems from the global asymptotic stability point of view. First of all, we classify the Kukles systems satisfying the assumptions: the origin is the unique equilibrium point which is locally asymptotically stable, and the divergence is negative except possibly at the origin. Then, for each of such Kukles system, we prove that the origin is globally asymptotically stable. Poincaré compactification is used to study the systems on the complements of compact sets.

确定平衡点吸引盆地的问题对于稳定性理论的应用非常重要。在本文中，我们解决了平面上一个常微分方程平衡点的全局渐近稳定性问题。更确切地说，我们从全局渐近稳定性的角度研究Kukles系统的平衡点。首先，我们对满足假设的Kukles系统进行分类：原点是唯一的平衡点，局部局部渐近稳定，并且散度为负（可能在原点除外）。然后，对于每个这样的Kukles系统，我们证明了原点是全局渐近稳定的。庞加莱压实用于研究紧定集补集上的系统。