### 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 |
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Title of host publication | Proceedings of the IEEE International Conference on Control Applications |

Pages | 83-88 |

Number of pages | 6 |

DOIs | |

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 |
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City | Saint Petersburg |

Period | 09/7/8 → 09/7/10 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks

AU - Ichikawa, Sho

AU - Ito, Yohei

AU - Uchida, Kenko

PY - 2009

Y1 - 2009

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.

UR - http://www.scopus.com/inward/record.url?scp=74049150015&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74049150015&partnerID=8YFLogxK

U2 - 10.1109/CCA.2009.5281071

DO - 10.1109/CCA.2009.5281071

M3 - Conference contribution

SN - 9781424446025

SP - 83

EP - 88

BT - Proceedings of the IEEE International Conference on Control Applications

ER -