Birth of limit cycles bifurcating from a nonsmooth center

作者：Buzzi Claudio A^*; de Carvalho Tiago; Teixeira Marco A

来源：Journal de Mathematiques Pures et Appliquees, 2014, 102(1): 36-47.

DOI：10.1016/j.matpur.2013.10.013

• Nonsmooth vector field
• Bifurcation
• Limit cycles
• Centers

This paper is concerned with a codimension analysis of a two-fold singularity of piecewise smooth planar vector fields, when it behaves itself like a center of smooth vector fields (also called nondegenerate Sigma-center). We prove that any nondegenerate Sigma-center is Sigma-equivalent to a particular normal form Z(0). Given a positive integer number k we explicitly construct families of piecewise smooth vector fields emerging from Z(0) that have k hyperbolic limit cycles bifurcating from the nondegenerate Sigma-center of Z(0) (the same holds for k = infinity). Moreover, we also exhibit families of piecewise smooth vector fields of codimension k emerging from Z(0). As a consequence we prove that Z(0) has infinite codimension.

• 出版日期2014-7