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Published 2010 | Published
Book Section - Chapter Open

Stability Analysis of a Class of Biological Network Models

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.

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