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A Model Checking Approach to Discrete Bifurcation Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9995))

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Abstract

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.

This work has been supported by the Czech Science Foundation grant GA15-11089S.

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Authors and Affiliations

  1. Systems Biology Laboratory, Faculty of Informatics, Masaryk University, Botanická 68a, 602 00, Brno, Czech Republic

    Nikola Beneš, Luboš Brim, Martin Demko, Samuel Pastva & David Šafránek

Authors
  1. Nikola Beneš
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  2. Luboš Brim
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  3. Martin Demko
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  4. Samuel Pastva
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  5. David Šafránek
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Corresponding author

Correspondence to Nikola Beneš .

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Editors and Affiliations

  1. Newcastle University, Newcastle upon Tyne, United Kingdom

    John Fitzgerald

  2. US Naval Research Laboratory, Washington, District of Columbia, USA

    Constance Heitmeyer

  3. ISTI-CNR, Pisa, Italy

    Stefania Gnesi

  4. University of Cyprus, Nicosia, Cyprus

    Anna Philippou

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Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D. (2016). A Model Checking Approach to Discrete Bifurcation Analysis. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds) FM 2016: Formal Methods. FM 2016. Lecture Notes in Computer Science(), vol 9995. Springer, Cham. https://doi.org/10.1007/978-3-319-48989-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-48989-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48988-9

  • Online ISBN: 978-3-319-48989-6

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