绝对复平衡动力系统
Absolutely complex balanced kinetic systems
摘要：
一个复平衡动力学系统是绝对复平衡的，如果每个正平衡点都是复平衡的。关于绝对络合物平衡的两个结果是现代化学反应网络理论（CRNT）的基础：Feinberg证明了任何亏零复平衡系统都是绝对复平衡的。同年，F。Horn和R.杰克逊证明了这个结果的（完全）逆命题是不正确的：任何复杂的平衡质量作用系统，不管它的不足，都是绝对复杂平衡的。本文给出了推广Horn和Jackson ACB定理的一些初步结果。特别是，我们专注于其他动力学系统的正缺陷，复杂的平衡意味着绝对复杂的平衡。同时，我们发现复杂平衡幂律反应物决定的动力学系统（PL-RDK）系统不是ACB。在我们寻找复平衡系统是绝对复平衡的充要条件时，我们遇到了所谓的CLP系统（具有期望的“对数参数化”性质的复平衡系统）。证明了具有双线性规划性质的复平衡系统是绝对复平衡的。对于非CLP系统，我们讨论了新的方法，找到充分条件ACB的动力学系统中含有非CLP系统：分解，正功能因子（PFF）和陪集相交计数（CIC）和它们的应用程序聚PL和Hill型系统。
英文摘要：
A complex balanced kinetic system is absolutely complex balanced (ACB) if every positive equilibrium is complex balanced. Two results on absolute complex balancing were foundational for modern chemical reaction network theory (CRNT): in 1972, M. Feinberg proved that any deficiency zero complex balanced system is absolutely complex balanced. In the same year, F. Horn and R. Jackson showed that the (full) converse of the result is not true: any complex balanced mass action system, regardless of its deficiency, is absolutely complex balanced. In this paper, we present initial results on the extension of the Horn and Jackson ACB Theorem. In particular, we focus on other kinetic systems with positive deficiency where complex balancing implies absolute complex balancing. While doing so, we found out that complex balanced power law reactant determined kinetic systems (PL-RDK) systems are not ACB. In our search for necessary and sufficient conditions for complex balanced systems to be absolutely complex balanced, we came across the so-called CLP systems (complex balanced systems with a desired "log parametrization" property). It is shown that complex balanced systems with bi-LP property are absolutely complex balanced. For non-CLP systems, we discuss novel methods for finding sufficient conditions for ACB in kinetic systems containing non-CLP systems: decompositions, the Positive Function Factor (PFF) and the Coset Intersection Count (CIC) and their application to poly-PL and Hill-type systems.
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