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

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Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. / Banaji, Murad; Craciun, Gheorghe.
In: Advances in Applied Mathematics, Vol. 44, No. 2, 28.02.2010, p. 168-184.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Banaji, M & Craciun, G 2010, 'Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems', Advances in Applied Mathematics, vol. 44, no. 2, pp. 168-184. https://doi.org/10.1016/j.aam.2009.07.003

APA

Banaji, M., & Craciun, G. (2010). Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Advances in Applied Mathematics, 44(2), 168-184. https://doi.org/10.1016/j.aam.2009.07.003

Vancouver

Banaji M, Craciun G. Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Advances in Applied Mathematics. 2010 Feb 28;44(2):168-184. doi: 10.1016/j.aam.2009.07.003

Author

Banaji, Murad ; Craciun, Gheorghe. / Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. In: Advances in Applied Mathematics. 2010 ; Vol. 44, No. 2. pp. 168-184.

Bibtex

@article{2617c80f8e1d4dcca111da62ed7508b7,
title = "Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems",
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 kinetics subject only to some weak natural constraints. 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.",
author = "Murad Banaji and Gheorghe Craciun",
year = "2010",
month = feb,
day = "28",
doi = "10.1016/j.aam.2009.07.003",
language = "English",
volume = "44",
pages = "168--184",
journal = "Advances in Applied Mathematics",
issn = "0196-8858",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems

AU - Banaji, Murad

AU - Craciun, Gheorghe

PY - 2010/2/28

Y1 - 2010/2/28

N2 - 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 kinetics subject only to some weak natural constraints. 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.

AB - 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 kinetics subject only to some weak natural constraints. 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.

U2 - 10.1016/j.aam.2009.07.003

DO - 10.1016/j.aam.2009.07.003

M3 - Journal article

VL - 44

SP - 168

EP - 184

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

IS - 2

ER -