Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives.

First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, …

Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential systems.

尽管已经有超过一千篇论文研究了平面二次微分系统及其应用，但我们仍然没有完全了解这些系统。在本文中，我们有两个目标。

首先，我们对二次系统的主要结果进行了简要的书目调查。在这里，我们不考虑这些系统在物理学、化学家、经济学、生物学等许多领域的应用……

其次，我们描述了一类新的平面可分离二次多项式微分系统。对于此类系统，我们提供了包含一个参数的范式，并使用庞加莱紧缩和膨胀技术，证明了可分离二次多项式微分系统在庞加莱圆盘中存在10个不等价的拓扑相图。