P matrix properties, injectivity, and stability in chemical reaction systems

Banaji, Murad, Donnell, Pete and Baigent, Stephen (2007) P matrix properties, injectivity, and stability in chemical reaction systems. SIAM Journal on Applied Mathematics, 67 (6). pp. 1523-1547. ISSN 0036-1399

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Abstract

In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain behaviour such as multiple equilibria, and sometimes implying stability. We first explore reaction systems and derive results which provide a deep connection between system structure and the P matrix property. We then examine a class of systems consisting of reactions coupled to an external rate-dependent negative feedback process, and characterise conditions which ensure the P matrix property survives the negative feedback. The techniques presented are applied to examples published in the mathematical and biological literature.

Item Type: Article
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 20848
Notes on copyright: This is the accepted manuscript the final article published as: SIAM Journal on Applied Mathematics, 2007, Vol. 67, No. 6 : pp. 1523-1547, P Matrix Properties, Injectivity, and Stability in Chemical Reaction Systems Murad Banaji, Pete Donnell, and Stephen Baigent (doi: 10.1137/060673412). Copyright © 2007 Society for Industrial and Applied Mathematics Read More: http://epubs.siam.org/doi/10.1137/060673412
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Depositing User: Murad Banaji
Date Deposited: 28 Oct 2016 08:15
Last Modified: 04 Apr 2019 05:27
URI: https://eprints.mdx.ac.uk/id/eprint/20848

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