Pseudo-Bautin Bifurcation in 3D Filippov Systems

Juan Castillo, Fernando Verduzco

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Consider a piecewise linear dynamical system in 3, divided by a switching plane, with the Teixeira Singularity (TS). Under the antiparallelism hypothesis, it is known that the system undergoes the so-called pseudo-Hopf bifurcation (pH). In this paper, we consider a particular position of the antiparallel vectors to yield a two-parametric unfolding of the TS. The bifurcation analysis gives us, besides the curve of pH bifurcation points, a curve of saddle-node bifurcation points for crossing limit cycles. We call this phenomenon the pseudo-Bautin bifurcation, since it exhibits the exact same behavior as the Bautin bifurcation for smooth dynamical systems.

Original languageEnglish
Article number2250120
JournalInternational Journal of Bifurcation and Chaos
Volume32
Issue number8
DOIs
StatePublished - 30 Jun 2022

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Keywords

  • Bautin bifurcation
  • Piecewise linear system
  • Saddle-node bifurcation for crossing limit cycle
  • Teixeira singularity

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