带两个区域的平面分段光滑系统的非双曲极限环分岔

Bifurcation of nonhyperbolic limit cycles in piecewise smooth planar systems with two zones

摘要:

本文讨论了一类含有两条切换线的平面分段光滑系统非双曲极限环的分岔. 假设该系统的未扰系统含有一个非双曲极限环且它分别与每一条切换线横截相交一次, 本文应用 Diliberto 定理和由此引出的变分引理导出了极限环的 Poincare映射, 并讨论了极限环的稳定性及其在扰动下的分岔.

Abstract:

In this paper we consider the bifurcation of nonhyperbolic limit cycles in a class of piecewise smooth planar systems with two zones. We assume that the unperturbed system has a nonhyperbolic limit cycle that crosses every switching line transversally exactly once. By using the Diliberto theorem and variation lemma we derive the Poincare map. Then we discuss the stability and bifurcation of the limit cycle.