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^*

^*Corresponding author for this work

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)

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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.",

author = "Sho Ichikawa and Yohei Ito and Kenko Uchida",

year = "2009",

doi = "10.1109/CCA.2009.5281071",

language = "English",

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AU - Ichikawa, Sho

AU - Ito, Yohei

AU - Uchida, Kenko

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N2 - 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.

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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AN - SCOPUS:74049150015

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BT - Proceedings of the IEEE International Conference on Control Applications

T2 - 2009 IEEE International Conference on Control Applications, CCA '09

Y2 - 8 July 2009 through 10 July 2009

ER -

Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks

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