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Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces

Research output: Contribution to journalArticle

Original languageEnglish
Article number1830020
JournalInternational Journal of Bifurcation and Chaos
Volume28
Issue number6
DOIs
DateAccepted/In press - 15 Mar 2018
DatePublished (current) - 15 Jun 2018

Abstract

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.

    Research areas

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

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via World Scientific at https://doi.org/10.1142/S0218127418300203 . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 6 MB, PDF document

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