Splitting reactions preserves nondegenerate behaviors in chemical reaction networks


Banaji, M. 2023. Splitting reactions preserves nondegenerate behaviors in chemical reaction networks. SIAM Journal on Applied Mathematics. 83 (2), pp. 748-769. https://doi.org/10.1137/22m1478392
TitleSplitting reactions preserves nondegenerate behaviors in chemical reaction networks
AuthorsBanaji, M.

A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following inheritance result is proved: under mild assumptions, splitting chemical reactions and inserting complexes involving some new chemical species preserves the capacity of a mass action CRN for multiple nondegenerate equilibria and/or periodic orbits. The claim has been proved previously for equilibria alone; however, the generalisation to include oscillation involves extensive development of rather different techniques. Several inheritance results for multistationarity and oscillation in mass action CRNs, including the main result of this paper, are gathered into a single theorem. Examples are presented showing how these results can be used together to make claims about reaction networks based on knowledge of their subnetworks. The examples include some networks of biological importance.

KeywordsApplied Mathematics, chemical reaction networks, oscillation, multistationarity, perturbation theory
Sustainable Development Goals9 Industry, innovation and infrastructure
PublisherSociety for Industrial and Applied Mathematics
JournalSIAM Journal on Applied Mathematics
Publication dates
Online28 Apr 2023
PrintApr 2023
Publication process dates
Deposited09 May 2023
Submitted15 Feb 2022
Accepted08 Nov 2022
Output statusPublished
Accepted author manuscript
Copyright Statement

Copyright © 2023 Society for Industrial and Applied Mathematics.
This is an accepted manuscript of a paper published in the SIAM Journal on Applied Mathematics in Vol. 83, Iss. 2 (2023), published by the Society for Industrial and Applied Mathematics (SIAM)

Web address (URL)https://epubs.siam.org/doi/10.1137/22M1478392
Digital Object Identifier (DOI)https://doi.org/10.1137/22m1478392
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