Pseudo-Bautin Bifurcation in 3D Filippov Systems

Juan Castillo, Fernando Verduzco

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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
Issue number8
StatePublished - 30 Jun 2022

Bibliographical note

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© 2022 World Scientific Publishing Company.


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


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