期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 219, 期 4, 页码 1449-1467出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2012.07.048
关键词
Jacobian criterion; Multiple steady states; Injectivity; Stoichiometric subspace; Degenerate steady state
资金
- Ministerio de Educacion'' of Spain
- Beatriu de Pinos'' from the Generalitat de Catalunya
- Ministerio de Ciencia e Innovacion [MTM2009-14163-C02-01]
- Lundbeck Foundation, Denmark
- Danish Research Councils
- Leverhulme Trust, UK
- Lundbeck Foundation [R49-2010-5841] Funding Source: researchfish
We study networks taken with mass-action kinetics and provide a Jacobian criterion that applies to an arbitrary network to preclude the existence of multiple positive steady states within any stoichiometric class for any choice of rate constants. We are concerned with the characterization of injective networks, that is, networks for which the species formation rate function is injective in the interior of the positive orthant within each stoichiometric class. We show that a network is injective if and only if the determinant of the Jacobian of a certain function does not vanish. The function consists of components of the species formation rate function and a maximal set of independent conservation laws. The determinant of the function is a polynomial in the species concentrations and the rate constants (linear in the latter) and its coefficients are fully determined. The criterion also precludes the existence of degenerate steady states. Further, we relate injectivity of a network to that of the network obtained by adding outflow, or degradation, reactions for all species. (C) 2012 Elsevier Inc. All rights reserved.
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