一类三次系统原点的奇点量与极限环分枝

The Singular Point and Limit Cycle Bifurcation of the Origin for a Class of Cubic System

运用奇点量理论和计算方法求出了一类三次系统原点的最高阶奇点量并证明为 5阶 ;由此解决了其原点的稳定性和可积性条件问题 ;作出此三次系统对应实系统的弱分枝函数并构造出其原点分枝出 5个极限环的具体形式。

According the theory of the singular point value and the calculating method, the highest singular point of the origin- 5th degree is obtained and proved for a class of cubic system.The problems of stability and integral condition of the origin are also solved.At the same time,the function of limit cycle bifurcation and the specific form with 5 cycles are created.