中文摘要：

研究一类五次Kukles系统原点的中心条件与极限环分支问题。借助计算机代数系统Mathematica,计算该系统对应的伴随复系统的前9个奇点量,得到该实系统原点为中心和9阶细焦点的充要条件,证明该Kukles系统在原点能分支出9个极限环。

英文摘要：

The center condition and limit cycles of the origin for a class of quintic Kukles systems are studied. Using the computer algebra system Mathematica, the first nine singular point values for the concomitant complex system of the real system is calculated. The necessary and sufficient conditions of the origin to be a center and a 9th-order weak focus point are obtained. It is proved that the Kukles system has 9 limit cycles around the origin.