### 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 | |

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)

## Fingerprint Dive into the research topics of 'Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the IEEE International Conference on Control Applications*(pp. 83-88). [5281071] https://doi.org/10.1109/CCA.2009.5281071