Regularisation of isolated codimension-2 discontinuity sets

Noah Cheesman, Kristian Uldall Kristiansen, S J Hogan

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalise to systems with higher codimension discontinuities. These higher order degeneracies occur in applications, with spatial Coulomb friction being the prominent example. In this work, we consider PWS systems with isolated codimension-2 discontinuity sets using regularization and blowup to study the dynamics. We present a general framework and give specific results for the local dynamics in a class of problems, and generalising Filippov sliding, crossing and sliding vector fields.
Original languageEnglish
JournalSIAM Journal on Applied Dynamical Systems
Publication statusUnpublished - 26 May 2021

Structured keywords

  • Engineering Mathematics Research Group


  • piece-wise smooth dynamical systems
  • regularisation
  • blowup
  • geometric singular perturbation theory
  • spatial Coulomb friction


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