An Analysis of a Circadian Model Using The Small-Gain Approach to Monotone Systems
Optimization and Control
2007-05-23 v1 Dynamical Systems
Quantitative Methods
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.
Keywords
Cite
@article{arxiv.math/0312062,
title = {An Analysis of a Circadian Model Using The Small-Gain Approach to Monotone Systems},
author = {David Angeli and Eduardo D. Sontag},
journal= {arXiv preprint arXiv:math/0312062},
year = {2007}
}
Comments
See http://www.math.rutgers.edu/~sontag/ for related work