研究一类五次系统:{dx/dt=-y(ax2+bx+1)+Dx-lx3+mx5 dy/dt=x(ax2+bx+1)我们计算了原点的焦点量,证明了原点至多为二阶细焦点,并且得到了原点是二阶细焦点时系统不存在极限环。
The limit cycle and focal value for a class for plane fifth polynomial system, which is {dx/dt=-y(ax2+bx+1)+Dx-lx3+mx5 dy/dt=x(ax2+bx+1),are discussed. The focal value of 0(0,0) is obeained, and it isproved that the origin is a 2 order of fine focus at most. There are no any limit cycles when O(0,0) is a 2 order of fine focus.