Regularization by External Variables

Conference paper
Part of the Trends in Mathematics book series (TM, volume 8)


Regularization was a big topic at the 2016 CRM Intensive Research Program on Advances in Nonsmooth Dynamics. There are many open questions concerning well known kinds of regularization (e.g., by smoothing or hysteresis). Here, we propose a framework for an alternative and important kind of regularization, by external variables that shadow either the state or the switch of the original system. The shadow systems are derived from and inspired by various applications in electronic control, predator-prey preference, time delay, and genetic regulation.


  1. 1.
    R. Edwards, A. Machina, G. McGregor, P. van den Driessche, A modelling framework for gene regulatory networks including transcription and translation. Bull. Math. Biol. 77, 953–983 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    P. Glendinning, M.R. Jeffrey, An introduction to piecewise smooth dynamics, Advanced Courses in Mathematics - CRM Barcelona (Springer, Berlin, 2016)Google Scholar
  3. 3.
    G. Kafanas, Sensor effects in sliding mode control of power conversion cells, this volumeGoogle Scholar
  4. 4.
    S. Piltz, Smoothing a piecewise-smooth: An example from plankton population dynamics, this volumeGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  3. 3.School of MathematicsUniversity of ManchesterManchesterUK
  4. 4.Department of Engineering MathematicsUniversity of BristolBristolUK

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