Limit cycles bifurcating from discontinuous centres

作者：Braga Denis de Carvalho; Carvalho Tiago; Mello Luis Fernando^*

来源：IMA Journal of Applied Mathematics, 2017, 82(4): 849-863.

DOI：10.1093/imamat/hxx017

• bifurcation
• limit cycle
• non-smooth vector field
• T-singularity
• two-fold singularity

In this article, we study limit cycles in discontinuous piecewise linear vector fields in R-2 and R-3. More precisely, we address the problem of understanding the dynamics around a degenerated two-fold singularity in R-2 and R-3, where it is also called T-singularity, which behave as discontinuous centres after suitable perturbations of the separation boundaries. We prove that, in both systems, it is possible to obtain k hyperbolic limit cycles bifurcating from these discontinuous centres, for any positive integer k. The same holds if k is infinity.

• 出版日期2017-8
• 单位Univ Estadual Paulista