具有一类双纽线解的三次系统

CUBIC SYSTEM WITH A CLASS OF A DOUBLE FOLIUM SOLUTION

给出了具有一类双纽线解①的三次系统的一般形状，提供了一般三次系统存在以双纽线①为分界线环的充要条件．并在参数平面上得到了具有双纽线解①时的一般三次系统所有可能的轨线的拓扑分类．

We give a general form of cubic system which possesses a class of double folium solution ①,and provide a necessary and sufficient condition for the existence of separatrix cycle,which is formed by the double folium ①in general cubic system.Further,we obtain the whole possible topological classification of the trajectories in the parameter plane of the general cubic system which possesses the double folium solution①.