TY - JOUR
T1 - Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces
AU - Tang , Xiaoxian
AU - Lin , Kexin
AU - Zhang , Zhishuo
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 564
EP - 600
PY - 2022
DA - 2022/08
SN - 3
DO - http://doi.org/10.4208/csiam-am.SO-2021-0044
UR - https://global-sci.org/intro/article_detail/csiam-am/20972.html
KW - Reaction networks, mass-action kinetics, multistationarity, multistability.
AB - <p style="text-align: justify;">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.</p>