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 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Mathematics(all)
Cite this
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 proceeding › Conference contribution
}
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 -