@article{Angeli:2009:10.1109/TAC.2007.911320,
author = {Angeli, D and Sontag, ED},
doi = {10.1109/TAC.2007.911320},
journal = {IEEE T AUTOMAT CONTR},
pages = {166--176},
title = {Oscillations in I/O Monotone Systems Under Negative Feedback},
url = {http://dx.doi.org/10.1109/TAC.2007.911320},
year = {2009}
}

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TY  - JOUR
AB  - Oscillatory behavior is a key property of many biological systems. The small-gain theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium, and hence its violation is a necessary condition for the existence of periodic solutions. One advantage of the use of the monotone SGT technique is its robustness with respect to all perturbations that preserve monotonicity and stability properties of a very low-dimensional (in many interesting examples, just one-dimensional) model reduction. This robustness makes the technique useful in the analysis of molecular biological models in which there is large uncertainty regarding the values of kinetic and other parameters. However, verifying the conditions needed in order to apply the SGT is not always easy. This paper provides an approach to the verification of the needed properties and illustrates the approach through an application to a classical model of circadian oscillations, as a nontrivial "case study," and provides a theorem in the converse direction of predicting oscillations when the SGT conditions fail.
AU  - Angeli,D
AU  - Sontag,ED
DO  - 10.1109/TAC.2007.911320
EP  - 176
PY  - 2009///
SN  - 0018-9286
SP  - 166
TI  - Oscillations in I/O Monotone Systems Under Negative Feedback
T2  - IEEE T AUTOMAT CONTR
UR  - http://dx.doi.org/10.1109/TAC.2007.911320
UR  - http://hdl.handle.net/10044/1/15422
ER  - 

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