A Model Checking Approach to Discrete Bifurcation Analysis

  • Nikola BenešEmail author
  • Luboš Brim
  • Martin Demko
  • Samuel Pastva
  • David Šafránek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9995)


Bifurcation analysis is a central task of the analysis of parameterised high-dimensional dynamical systems that undergo transitions as parameters are changed. The classical numerical and analytical methods are typically limited to a small number of system parameters. In this paper we propose a novel approach to bifurcation analysis that is based on a suitable discrete abstraction of the system and employs model checking for discovering critical parameter values, referred to as bifurcation points, for which various kinds of behaviour (equilibrium, cycling) appear or disappear. To describe such behaviour patterns, called phase portraits, we use a hybrid version of a CTL logic augmented with direction formulae. We demonstrate the method on a case study taken from systems biology.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Nikola Beneš
    • 1
    Email author
  • Luboš Brim
    • 1
  • Martin Demko
    • 1
  • Samuel Pastva
    • 1
  • David Šafránek
    • 1
  1. 1.Systems Biology Laboratory, Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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