An Analysis of a Circadian Model Using The Small-Gain Approach to Monotone Systems
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- December 2003
- DOI:
- 10.48550/arXiv.math/0312062
- arXiv:
- arXiv:math/0312062
- Bibcode:
- 2003math.....12062A
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Dynamical Systems;
- Quantitative Biology - Quantitative Methods
- E-Print:
- See http://www.math.rutgers.edu/~sontag/ for related work