Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks

Sho Ichikawa, Yohei Ito, Kenko Uchida

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    4 Citations (Scopus)

    Abstract

    The Lyapunov equation, which describes stochastic variations of systems as a covariance equation, plays a central role in evaluation and prediction of behavior of genetic regulatory networks fluctuated by molecular noises. When the genetic network is an autonomously oscillatory system, the Lyapunov equation becomes a periodic differential equation that has generally unbounded solutions. We discuss orbital stability and periodicity properties of the solutions to the periodic Lyapunov differential equation by using Floquet-Lyapunov theory, and propose two global measures for evaluating stochastic fluctuations of the whole periodic trajectory. We also provide an evaluation formula for the period fluctuation.

    Original languageEnglish
    Title of host publicationProceedings of the IEEE International Conference on Control Applications
    Pages83-88
    Number of pages6
    DOIs
    Publication statusPublished - 2009
    Event2009 IEEE International Conference on Control Applications, CCA '09 - Saint Petersburg
    Duration: 2009 Jul 82009 Jul 10

    Other

    Other2009 IEEE International Conference on Control Applications, CCA '09
    CitySaint Petersburg
    Period09/7/809/7/10

    Fingerprint

    Lyapunov Equation
    Genetic Network
    Differential equations
    Differential equation
    Evaluation
    Fluctuations
    Unbounded Solutions
    Orbital Stability
    Periodic Trajectories
    Genetic Regulatory Networks
    Floquet Theory
    Lyapunov Theory
    Trajectories
    Periodicity
    Prediction

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Computer Science Applications
    • Mathematics(all)

    Cite this

    Ichikawa, S., Ito, Y., & Uchida, K. (2009). Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks. In Proceedings of the IEEE International Conference on Control Applications (pp. 83-88). [5281071] https://doi.org/10.1109/CCA.2009.5281071

    Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks. / Ichikawa, Sho; Ito, Yohei; Uchida, Kenko.

    Proceedings of the IEEE International Conference on Control Applications. 2009. p. 83-88 5281071.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Ichikawa, S, Ito, Y & Uchida, K 2009, Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks. in Proceedings of the IEEE International Conference on Control Applications., 5281071, pp. 83-88, 2009 IEEE International Conference on Control Applications, CCA '09, Saint Petersburg, 09/7/8. https://doi.org/10.1109/CCA.2009.5281071
    Ichikawa S, Ito Y, Uchida K. Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks. In Proceedings of the IEEE International Conference on Control Applications. 2009. p. 83-88. 5281071 https://doi.org/10.1109/CCA.2009.5281071
    Ichikawa, Sho ; Ito, Yohei ; Uchida, Kenko. / Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks. Proceedings of the IEEE International Conference on Control Applications. 2009. pp. 83-88
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