化学反应网络非退化多平稳性的遗传
The inheritance of nondegenerate multistationarity in chemical reaction networks
摘要：
研究了化学反应网络（CRN）中允许多重正非退化平衡点（MPNE）和多重正线性稳定平衡点（MPSE）的性质是如何遗传的。具体地说，我们什么时候可以根据对CRN子网的分析推断出CRN允许MPNE或MPSE？使用分析中的基本技术，我们能够确定在构建网络时MPNE和MPSE继承的许多情况。其中一些修改是已知的，而其他的是新的，但所有的结果都证明使用相同的基本框架，我们相信将产生进一步的结果。结果主要是质量作用动力学，虽然与自然，在某些情况下，立即，概括到其他类别的动力学。
英文摘要：
We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction networks (CRNs). Specifically, when is it that we can deduce that a CRN admits MPNE or MPSE based on analysis of its subnetworks? Using basic techniques from analysis we are able to identify a number of situations where MPNE and MPSE are inherited as we build up a network. Some of these modifications are known while others are new, but all results are proved using the same basic framework, which we believe will yield further results. The results are presented primarily for mass action kinetics, although with natural, and in some cases immediate, generalisation to other classes of kinetics.
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