Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces

Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces

Year:    2022

Author:    Xiaoxian Tang, Kexin Lin, Zhishuo Zhang

CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 3 : pp. 564–600

Abstract

We study the multistationarity for the reaction networks with one dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We provide a necessary condition for a network to admit multistationarity in terms of the stoichiometric coefficients, which can be described by “arrow diagrams”. This necessary condition is not sufficient unless there exist two reactions in the network such that the subnetwork consisting of the two reactions admits at least one and finitely many positive steady states. We also prove that if a network admits at least three positive steady states, then it contains at least three “bi-arrow diagrams”. More than that, we completely characterize the bi-reaction networks that admit at least three positive steady states.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.SO-2021-0044

CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 3 : pp. 564–600

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    37

Keywords:    Reaction networks mass-action kinetics multistationarity multistability.

Author Details

Xiaoxian Tang

Kexin Lin

Zhishuo Zhang