An Analysis of a Circadian Model Using The Small-Gain Approach to Monotone Systems

Details An Analysis of a Circadian Model Using The Small-Gain Approach to Monotone Systems An Analysis of a Circadian Model Using The Small-Gain Approach to Monotone Systems

2003-12-02

arxiv.org/abs/math/0312062v1

Mathematics

Optimization and Control

See http://www.math.rutgers.edu/~sontag/ for related work

Scientific paper

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.

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