## Abstract

We consider linear elimination of variables in the steady state equations of a chem- ical reaction network. Particular subsets of variables corresponding to sets of so-called reactant- noninteracting species, are introduced. The steady state equations for the variables in such a set, taken together with potential linear conservation laws in the variables, define a linear system of equa- tions. We give conditions that guarantee that the solution to this system is nonnegative, provided it is unique. The results are framed in terms of spanning forests of a particular multidigraph derived from the reaction network and thereby conditions for uniqueness and nonnegativity of a solution are derived by means of the multidigraph. Though our motivation comes from applications in systems biology, the results have general applicability in applied sciences.

Original language | English |
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Journal | SIAM Journal on Applied Mathematics |

Volume | 79 |

Issue number | 6 |

Pages (from-to) | 2434-2455 |

ISSN | 0036-1399 |

DOIs | |

Publication status | Published - 2019 |

## Keywords

- Elimination
- Linear system
- Noninteracting
- Positive solution
- Spanning forest