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We study the multistationarity for the reaction networks with one-dimensionalstoichiometric subspaces, and we focus on the networks admitting finitely manypositive steady states. We prove that if a network admits multistationarity,then network has an embedded one-species network with arrow diagram (->,<-) andanother with arrow diagram (<-,->). The inverse is also true if there exist tworeactions in the network such that the subnetwork consisting of the tworeactions admits at least one and finitely many positive steady states. We alsoprove that if a network admits at least three positive steady states, then itcontains at least three bi-arrow diagrams. More than that, we completelycharacterize the bi-reaction networks that admit at least three positive steadystates.

Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces