Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces (CSIAM Transactions on Applied Mathematics, 2022)
We study the multistationarity for the reaction networks with one dimensional stoichiometric subspaces, and we focus on the networks admitting finitely manypositive 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 admitsat least one and finitely many positive steady states. We also prove that if a networkadmits at least three positive steady states, then it contains at least three “bi-arrowdiagrams”. More than that, we completely characterize the bi-reaction networks thatadmit at least three positive steady states.