NDLI: Periodic Lyapunov differential equation for noise evaluation in oscillatory genetic networks

Content Provider	IEEE Xplore Digital Library
Author	Ichikawa, S. Ito, Y. Uchida, K.
Copyright Year	2009
Description	Author affiliation: Department of Electrical Engineering and Bioscience, Waseda University, Tokyo 169-8555, Japan (Ichikawa, S.; Ito, Y.; Uchida, K.)
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.
Starting Page	83
Ending Page	88
File Size	363978
Page Count	6
File Format	PDF
ISBN	9781424446018
ISSN	10851992
DOI	10.1109/CCA.2009.5281071
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-07-08
Publisher Place	Russia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Differential equations Genetics Fluctuations Stochastic resonance Control systems Stability Indium tin oxide Extraterrestrial measurements Predictive models Stochastic systems
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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