Stability Analysis of a Class of Biological Network Models
- Creators
- Motee, Nader
- Bamieh, Bassam
- Khammash, Mustafa
Abstract
In this paper, we establish stability conditions for a special class of interconnected systems arisen in several biochemical applications. It is known that most of the biochemical processes can be represented using quasi-polynomial systems. We show that a special class of quasi-polynomial systems can be cast in the Lotka-Volterra canonical form. We study the asymptotic stability properties of a class of quasipolynomial systems which are relevant to biological network models. First, we show that under some sufficient conditions the solutions of the quasi-polynomial systems (in the positive orthant) converge to the set of equilibrium points. These results are applied to parameterized models of three different biological systems: generalized mass action (GMA) model, an oscillating biochemical network, and a reduced order model with Hill function. We show that one can find the range of parameters for which a given parameterized model is stable.
Additional Information
© 2010 AACC. Issue Date: June 30 2010-July 2 2010. Date of Current Version: 29 July 2010. This work is supported by research funding from the National Science Foundation through Grants ECCS-0835847 and ECCS-0802008 and funding from the NIH through grant R01-GM04983 and the Institute for Collaborative Biotechnologies through Grant DAAD19-03-D-0004 from the US Army Research Office.Attached Files
Published - Motee2010p134352009_American_Control_Conference_Vols_1-9.pdf
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Additional details
- Eprint ID
- 23292
- Resolver ID
- CaltechAUTHORS:20110413-070209370
- ECCS-0835847
- NSF
- ECCS-0802008
- NSF
- R01-GM04983
- NIH
- DAAD19-03-D-0004
- Army Research Office (ARO) Institute for Collaborative Biotechnologies
- Created
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2011-05-25Created from EPrint's datestamp field
- Updated
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2020-03-09Created from EPrint's last_modified field
- Series Name
- Proceedings of the American Control Conference
- Other Numbering System Name
- INSPEC Accession Number
- Other Numbering System Identifier
- 11508824