Determining the structural properties of a class of biological models

Franco Blanchini; Elisa Franco; Giulia Giordano

doi:10.1109/CDC.2012.6427037

Determining the structural properties of a class of biological models

Franco Blanchini^*, Elisa Franco, Giulia Giordano

^*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

19 Citations (Scopus)

Abstract

A property for a class of systems is said to be structural if it is met by any system in the class regardless of the adopted parameters. In this paper we investigate the structural nature of oscillatory behaviors, adaptation and monotonicity in a class of sign-invariant systems, capturing a wide variety of biological models. We employ standard robustness analysis tools, suitably tailored to the category of sign definite dynamics, i.e. in which terms are monotonic with respect to all arguments. In particular, our results are based on Jacobian analysis and invariant sets, and we are able to provide simple criteria to determine whether a system structurally admits Hopf-type bifurcations, perfect adaptation or monotonic behavior. Such criteria are easily verified numerically on a set of examples.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Pages	5505-5510
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2012.6427037
Publication status	Published - 1 Dec 2012
Externally published	Yes

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

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10.1109/CDC.2012.6427037

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Determining the structural properties of a class of biological models. / Blanchini, Franco; Franco, Elisa; Giordano, Giulia.
Proceedings of the IEEE Conference on Decision and Control. 2012. p. 5505-5510 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AB - A property for a class of systems is said to be structural if it is met by any system in the class regardless of the adopted parameters. In this paper we investigate the structural nature of oscillatory behaviors, adaptation and monotonicity in a class of sign-invariant systems, capturing a wide variety of biological models. We employ standard robustness analysis tools, suitably tailored to the category of sign definite dynamics, i.e. in which terms are monotonic with respect to all arguments. In particular, our results are based on Jacobian analysis and invariant sets, and we are able to provide simple criteria to determine whether a system structurally admits Hopf-type bifurcations, perfect adaptation or monotonic behavior. Such criteria are easily verified numerically on a set of examples.

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Determining the structural properties of a class of biological models

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