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Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes

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  • Daniel Silk

    (Centre for Bioinformatics, Imperial College London, London SW7 2AZ, UK.
    Institute of Mathematical Sciences, Imperial College London, London SW7 2AZ, UK.)

  • Paul D.W. Kirk

    (Centre for Bioinformatics, Imperial College London, London SW7 2AZ, UK.
    Institute of Mathematical Sciences, Imperial College London, London SW7 2AZ, UK.)

  • Chris P. Barnes

    (Centre for Bioinformatics, Imperial College London, London SW7 2AZ, UK.
    Institute of Mathematical Sciences, Imperial College London, London SW7 2AZ, UK.)

  • Tina Toni

    (Centre for Bioinformatics, Imperial College London, London SW7 2AZ, UK.
    Institute of Mathematical Sciences, Imperial College London, London SW7 2AZ, UK.
    Centre for Integrative Systems Biology at Imperial College London, London SW7 2AZ, UK.
    Present address: Department for Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.)

  • Anna Rose

    (Centre for Integrative Systems Biology at Imperial College London, London SW7 2AZ, UK.
    Imperial College London, London SW7 2AZ, UK.)

  • Simon Moon

    (Centre for Integrative Systems Biology at Imperial College London, London SW7 2AZ, UK.)

  • Margaret J. Dallman

    (Centre for Integrative Systems Biology at Imperial College London, London SW7 2AZ, UK.
    Imperial College London, London SW7 2AZ, UK.)

  • Michael P.H. Stumpf

    (Centre for Bioinformatics, Imperial College London, London SW7 2AZ, UK.
    Institute of Mathematical Sciences, Imperial College London, London SW7 2AZ, UK.
    Centre for Integrative Systems Biology at Imperial College London, London SW7 2AZ, UK.
    Institute of Chemical Biology, Imperial College London, London SW7 2AZ, UK.)

Abstract

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems.

Suggested Citation

  • Daniel Silk & Paul D.W. Kirk & Chris P. Barnes & Tina Toni & Anna Rose & Simon Moon & Margaret J. Dallman & Michael P.H. Stumpf, 2011. "Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes," Nature Communications, Nature, vol. 2(1), pages 1-6, September.
    • Handle: RePEc:nat:natcom:v:2:y:2011:i:1:d:10.1038_ncomms1496
    DOI: 10.1038/ncomms1496
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    Cited by:

    1. Žurauskienė, Justina & Kirk, Paul & Thorne, Thomas & Stumpf, Michael P.H., 2014. "Bayesian non-parametric approaches to reconstructing oscillatory systems and the Nyquist limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 33-42.
    2. Juliane Liepe & Sarah Filippi & Michał Komorowski & Michael P H Stumpf, 2013. "Maximizing the Information Content of Experiments in Systems Biology," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-13, January.
    3. Filippi Sarah & Barnes Chris P. & Stumpf Michael P.H. & Cornebise Julien, 2013. "On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 87-107, March.

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