带多个切换的Filippov系统极限环在扰动下的保持性

Persistence of limit cycles in Filippov systems with multiple switching lines

本文讨论了一类含有有限多条切换线的平面Filippov系统极限环在扰动下的保持性.假设该类平面Filippov系统的未扰系统含有一个极限环且它分别与每一条切换线横截相交一次,作者应用Diliberto定理和由此引出的变分引理导出了极限环的特征指标的计算公式,并利用该公式讨论了系统极限环的稳定性及其在扰动下保持的条件.

In this paper we discuss the persistence of the limit cycle in a class of planar Filippov systems with multiple switching lines. The authors assume that the unperturbed system of the planar Filippov systems has a limit cycle that crosses every switching line transversally exactly once. By using Diliberto Theorem and Variation Lemma we derived the formula for the characteristic exponent. Then we give a condition for the stability and persistence of the limit cycle.