The Regularized Visible Fold Revisited

Research output: Contribution to journalJournal articleResearchpeer-review

27 Downloads (Pure)


The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter ϵ→0. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit ϵ→0, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law.
Original languageEnglish
JournalJournal of Nonlinear Science
Pages (from-to)2463–2511
Publication statusPublished - 2020


  • Blowup
  • Geometric singular perturbation theory
  • Piecewise smooth systems
  • Piecewise smooth bifurcations
  • Friction
  • Grazing bifurcations


Dive into the research topics of 'The Regularized Visible Fold Revisited'. Together they form a unique fingerprint.

Cite this