Birth of limit cycles bifurcating from a nonsmooth center

Author(s)

Buzzi, Claudio A. ^[1] ; de Carvalho, Tiago ^[2] ; Teixeira, Marco A. ^[3]

Affiliation

^[1] IBILCE UNESP, BR-15054000 Sao Paulo - Brazil

^[2] FC UNESP, BR-17033360 Sao Paulo - Brazil

^[3] IMECC UNICAMP, BR-13081970 Sao Paulo - Brazil

• Document type: Journal article
• Source: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 102, n. 1, p. 36-47, JUL 2014.
• Web of Science Citations: 16

Abstract

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. (c) 2013 Elsevier Masson SAS. All rights reserved. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/00481-6 - Regularization, singular perturbation and Averaging method applied to piecewise smooth vector fields
• Grantee: Tiago de Carvalho
• Support Opportunities: Regular Research Grants