标题： 哪些小反应网络是多稳态的？ 显示英文标题

标题： Which small reaction networks are multistationary?

摘要： 带有质量作用动力学的反应网络出现在许多环境中，从流行病学到种群生物学再到化学反应系统。 双稳态反应网络被认为构成了生物化学开关的基础，这引出了以下问题：哪些反应网络具有多个稳态的潜力？ 数学上，这相当于问：在某些参数化的多项式系统家族中，哪些系统具有多个正根？ 目前还没有完整的答案。 这项工作分析了最小的网络，即只有少数化学物质或反应的网络。 对于这些“最小”网络，我们完全回答了多稳态的问题，在某些情况下还回答了多稳定性的问题，从而扩展了Boros的相关工作。 我们的结果突出了反应网络的牛顿多面体（反应向量的凸包）所起的作用。 此外，我们的工作受到最近结果的启发，这些结果解释了给定网络的多稳态能力如何来源于某些通常更小的相关网络的多稳态能力。 因此，我们对分类小型多稳态网络感兴趣，而我们的工作是朝着这个方向迈出的第一步。 显示英文摘要

摘要： Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the following question: which reaction networks have the capacity for multiple steady states? Mathematically, this asks: among certain parametrized families of polynomial systems, which admit multiple positive roots? No complete answer is known. This work analyzes the smallest networks, those with only a few chemical species or reactions. For these "smallest" networks, we completely answer the question of multistationarity and, in some cases, multistability too, thereby extending related work of Boros. Our results highlight the role played by the Newton polytope of a network (the convex hull of the reactant vectors). Also, our work is motivated by recent results that explain how a given network's capacity for multistationarity arises from that of certain related networks which are typically smaller. Hence, we are interested in classifying small multistationary networks, and our work forms a first step in this direction.