Algebraic approaches for the decomposition of reaction networks and the determination of existence and number of steady states

Joseph M Sauder; Bruce P Ayati; Ryan Kinser

doi:10.48550/arxiv.2503.01179

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Algebraic approaches for the decomposition of reaction networks and the determination of existence and number of steady states

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Algebraic approaches for the decomposition of reaction networks and the determination of existence and number of steady states

Joseph M Sauder, Bruce P Ayati and Ryan Kinser

ArXiV.org

Cornell University

03/02/2025

DOI: 10.48550/arxiv.2503.01179

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https://doi.org/10.48550/arxiv.2503.01179View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks is the reliance on explicit parameter values which in many cases cannot be determined experimentally. This can make analyzing a dynamical system infeasible, particularly when the size of the system is large. One approach is to analyze subnetworks of the full network and use the results for a full analysis. Our focus is on the equilibria of reaction networks. Gröbner basis computation is a useful approach for solving the polynomial equations which correspond to equilibria of a dynamical system. We identify a class of networks for which Gröbner basis computations of subnetworks can be used to reconstruct the more expensive Gröbner basis computation of the whole network. We compliment this result with tools to determine if a steady state can exist, and if so, how many.

Quantitative Biology - Quantitative Methods

Details

Title: Subtitle: Algebraic approaches for the decomposition of reaction networks and the determination of existence and number of steady states
Creators: Joseph M Sauder - University of Iowa
Bruce P Ayati - University of Iowa
Ryan Kinser - University of Iowa
Resource Type: Preprint
Publication Details: ArXiV.org
DOI: 10.48550/arxiv.2503.01179
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 03/02/2025
Academic Unit: Mathematics
Record Identifier: 9984797930602771

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