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)
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Ichikawa, S., Ito, Y., & Uchida, K. (2009). Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks. In Proceedings of the IEEE International Conference on Control Applications (pp. 83-88). [5281071] https://doi.org/10.1109/CCA.2009.5281071