论文标题
分裂反应保留了化学反应网络中非排定行为
Splitting reactions preserves nondegenerate behaviours in chemical reaction networks
论文作者
论文摘要
一个被称为遗传结果的结果家族告诉我们，化学反应网络（CRN）的哪些扩大保持其非平凡行为的能力，例如多立场性和振荡。在本文中，证明了以下遗传结果：在温和的假设下，将化学反应分裂并插入涉及某些新化学物种的复合物可保留多个非排定平衡和/或周期性轨道的质量作用CRN的能力。该主张先前仅证明了平衡。但是，包括振荡的概括涉及相当不同的技术的广泛发展。在包括本文的主要结果在内的群众行动CRN中多立法性和振荡的几种遗传结果被收集到单个定理中。示出了示例，显示了如何将这些结果一起使用，以根据其子网知识对反应网络提出主张。这些示例包括一些生物学重要性的网络。
A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following inheritance result is proved: under mild assumptions, splitting chemical reactions and inserting complexes involving some new chemical species preserves the capacity of a mass action CRN for multiple nondegenerate equilibria and/or periodic orbits. The claim has been proved previously for equilibria alone; however, the generalisation to include oscillation involves extensive development of rather different techniques. Several inheritance results for multistationarity and oscillation in mass action CRNs, including the main result of this paper, are gathered into a single theorem. Examples are presented showing how these results can be used together to make claims about reaction networks based on knowledge of their subnetworks. The examples include some networks of biological importance.
