标题： 反应网络在二维计量空间中的多稳态性 显示英文标题

标题： Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces

摘要： 我们研究具有二维计量子空间的反应网络的多稳态，并关注那些具有有限多个正平衡态的网络。 我们证明，如果一个网络存在多稳态，则该网络包含一个嵌入的一物种网络，其箭头图示为 (->,<-)，以及另一个箭头图示为 (<-,->) 的网络。 如果网络中存在两个反应，且由这两个反应组成的子网络至少有一个且有限多个正平衡态，则上述结论的逆命题也成立。 我们还证明，如果一个网络至少有三个正平衡态，则它至少包含三个双箭头图示。 此外，我们完全表征了至少具有三个正平衡态的双反应网络。 显示英文摘要

摘要： 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 prove that if a network admits multistationarity, then network has an embedded one-species network with arrow diagram (->,<-) and another with arrow diagram (<-,->). The inverse is also true if 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.