Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 72, Issue 4, Pages 959-981Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110847305
Keywords
semiflow; species graph; noninteracting; spanning tree; polynomial equations
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Funding
- Ministerio de Educacion of Spain
- Ministerio de Ciencia e Innovacion [MTM2009-14163-C02-01]
- Danish Research Council
- Lundbeck Foundation, Denmark
- Leverhulme Trust, UK
- Lundbeck Foundation [R49-2010-5841] Funding Source: researchfish
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We consider chemical reaction networks taken with mass-action kinetics. The steady states of such a system are solutions to a system of polynomial equations. Even for small systems the task of finding the solutions is daunting. We develop an algebraic framework and procedure for linear elimination of variables. The procedure reduces the variables in the system to a set of core variables by eliminating variables corresponding to a set of noninteracting species. The steady states are parameterized algebraically by the core variables, and a graphical condition is given that ensures that a steady state with positive core variables necessarily takes positive values for all variables. Further, we characterize graphically the sets of eliminated variables that are constrained by a conservation law and show that this conservation law takes a specific form.
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