Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks

Sho Ichikawa; Yohei Ito; Kenko Uchida

doi:10.1109/CCA.2009.5281071

Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks

Sho Ichikawa, Yohei Ito, Kenko Uchida

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Proceedings of the IEEE International Conference on Control Applications
Pages	83-88
Number of pages	6
DOIs	https://doi.org/10.1109/CCA.2009.5281071
Publication status	Published - 2009
Event	2009 IEEE International Conference on Control Applications, CCA '09 - Saint Petersburg Duration: 2009 Jul 8 → 2009 Jul 10

Other

Other	2009 IEEE International Conference on Control Applications, CCA '09
City	Saint Petersburg
Period	09/7/8 → 09/7/10

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Mathematics(all)

Access to Document

10.1109/CCA.2009.5281071

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title = "Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks",

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.",

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language = "English",

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AU - Ito, Yohei

AU - Uchida, Kenko

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AB - 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.

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BT - Proceedings of the IEEE International Conference on Control Applications

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