dorsal/arxiv
View SchemaOscillations in I/O monotone systems under negative feedback
| Authors | David Angeli, Eduardo D. Sontag |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0701018 |
| URL | https://arxiv.org/abs/q-bio/0701018 |
Abstract
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 also provides a theorem in the converse direction of predicting oscillations when the SGT conditions fail.
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"abstract": "Oscillatory behavior is a key property of many biological systems. The\nSmall-Gain Theorem (SGT) for input/output monotone systems provides a\nsufficient condition for global asymptotic stability of an equilibrium and\nhence its violation is a necessary condition for the existence of periodic\nsolutions. One advantage of the use of the monotone SGT technique is its\nrobustness with respect to all perturbations that preserve monotonicity and\nstability properties of a very low-dimensional (in many interesting examples,\njust one-dimensional) model reduction. This robustness makes the technique\nuseful in the analysis of molecular biological models in which there is large\nuncertainty regarding the values of kinetic and other parameters. However,\nverifying the conditions needed in order to apply the SGT is not always easy.\nThis paper provides an approach to the verification of the needed properties,\nand illustrates the approach through an application to a classical model of\ncircadian oscillations, as a nontrivial ``case study,\u0027\u0027 and also provides a\ntheorem in the converse direction of predicting oscillations when the SGT\nconditions fail.",
"arxiv_id": "q-bio/0701018",
"authors": [
"David Angeli",
"Eduardo D. Sontag"
],
"categories": [
"q-bio.QM",
"q-bio.MN"
],
"title": "Oscillations in I/O monotone systems under negative feedback",
"url": "https://arxiv.org/abs/q-bio/0701018"
},
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