期刊
JOURNAL OF NONLINEAR SCIENCE
卷 18, 期 5, 页码 527-550出版社
SPRINGER
DOI: 10.1007/s00332-008-9021-2
关键词
Singular perturbation; Monotone systems; Asymptotic stability; MAPK system
资金
- NSF [DMS-0614371]
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation futile cycle motif which plays a central role in eukaryotic cell signaling.
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