Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces

M. R. Jeffrey, G. Kafanas, D. J.W. Simpson

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

14 Citations (Scopus)
361 Downloads (Pure)


Differential equations that switch between different modes of behavior across a surface of discontinuity are used to model, for example, electronic switches, mechanical contact, predator-prey preference changes, and genetic or cellular regulation. Switching in such systems is unlikely to occur precisely at the ideal discontinuity surface, but instead can involve various spatiotemporal delays or noise. If a system switches between more than two modes, across a boundary formed by the intersection of discontinuity surfaces, then its motion along that intersection becomes highly sensitive to such nonidealities. If switching across the surfaces is affected by hysteresis, time delay, or discretization, then motion along the intersection can be affected by erratic variations that we characterize as "jitter". Introducing noise, or smoothing out the discontinuity, instead leads to steady motion along the intersection well described by the so-called canopy extension of Filippov's sliding concept (which applies when the discontinuity surface is a simple hypersurface). We illustrate the results with numerical experiments and an example from power electronics, providing explanations for the phenomenon as far as they are known.

Original languageEnglish
Article number1830020
JournalInternational Journal of Bifurcation and Chaos
Issue number6
Publication statusPublished - 15 Jun 2018

Structured keywords

  • Engineering Mathematics Research Group


  • Discontinuity
  • dynamics
  • intersection
  • jitter
  • modeling
  • sliding
  • switching


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