Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems

Banaji, Murad and Craciun, Gheorghe (2009) Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Advances in Applied Mathematics, 44 (2). pp. 168-184. ISSN 0196-8858 (doi:10.1016/j.aam.2009.07.003)

[img]
Preview
PDF - Final accepted version (with author's formatting)
Download (245kB) | Preview

Abstract

In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.

Item Type: Article
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 20586
Depositing User: Murad Banaji
Date Deposited: 23 Sep 2016 10:34
Last Modified: 03 Jun 2019 15:13
URI: https://eprints.mdx.ac.uk/id/eprint/20586

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year