平面分段线性系统的极限环折分支

Fold Bifurcation of Limit Cycles in a Planar Piecewise Linear System

该文考虑了以半折线的旋转角θ为参数的鞍-鞍型平面分段线性系统.通过拓扑变换将该系统转化为折线边界的参数系统,然后通过定义在正y-半轴上的庞加莱映射和分支理论,得到了极限环折分支产生的条件.

In this paper we consider planar piecewise linear systems of saddle-saddle type with parameter the rotation angleθof half separation line.We transform such a system to a parameter system with a nonregular separation line by a topological transformation,and then obtain several conditions for the occurence of fold bifurcation of limit cycles through Poincarémaps defined on the positive y-axis and the theory of bifurcations.