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Abstract: In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory establishes global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter. This stability persists even under arbitrary delays in the feedback loop. (Update)
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BibTeX entry: (Update)
Angeli D, Sontag E (2003) An analysis of a circadian model using the small-gain approach to monotone systems, arXiv.OC/0312062, Dec 2003 http://citeseer.ist.psu.edu/angeli03analysis.html More
@misc{ angeli03analysis,
author = "D. Angeli and E. Sontag",
title = "An analysis of a circadian model using the small-gain approach to monotone
systems",
text = "Angeli D, Sontag E (2003) An analysis of a circadian model using the small-gain
approach to monotone systems, arXiv.OC/0312062, Dec 2003",
year = "2003",
url = "citeseer.ist.psu.edu/angeli03analysis.html" }
Citations (may not include all citations):16 Monotone Dynamical Systems: an Introduction to the Theory of.. (context) - Smith - 1995
9 Monotone control systems - Angeli, Sontag - 2003
8 Competitive and cooperative tridiagonal systems of different.. (context) - Smillie - 1984
8 Periodic tridiagonal competitive and cooperative systems of .. (context) - Smith - 1991
6 Biochemical Oscillations and Cellular Rhythms (context) - Goldbeter - 1996
6 A model for circadian oscillations in the Drosophila period .. (context) - Goldbeter - 1995
4 Multi-stability in monotone Input /Output systems (context) - Angeli, Sontag - 2003
3 Detection of multistability, bifurcations, and hysteresis in.. (context) - Angeli, Ferrell et al. - 2004
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