一类三次平面自治系统的异宿环分支

The Bifurcation of the Heteroelinic Loop in a Cubic Autonomous System

对一类给定的三次多项式系统,寻找该系统的一类特殊代数不变曲线,得到这些代数不变曲线为异宿轨线的条件;并分析该系统的奇点.讨论了闭轨线的存在性问题,得到系统在相平面的单位圆盘K-上的全局结构,从而得出相图随参数变化的情况.

According to a plane autonomous system, this paper considers seeking its a special algebra invariant curve to get the condition of these curves being heteroelinic orbits. Then by way of the analysis of the singularities and the discussion about the existence of a closed-orbit, it obtains the global topological structure of phase-portraits of this system. Finally, it obtains the variation of the phase-portraits with the varying of the parameter.