In this paper, we obtain a necessary and sufficient condition for the existence of a parabolic separatrix that connects a saddle-node point with a hyperbolic saddle point in a class of systems, which gave premise condition to analytic study semi-local bifurcation of a separatrix connecting a saddle-node point with a hyperbolic saddle point.
讨论了一类系统存在鞍结点分界线与双曲鞍点连线的条件,得出鞍结点分界线与双曲鞍点连线是对称轴平行于y轴的抛物线的充要条件,为研究这类系统存在鞍结点分界线与双曲鞍点连线的半局部分支提供了前提条件。