This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the “Multistationarity Algorithm for PLK systems” (MSA), combines (i) the extension of the “higher deficiency algorithm” of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg’s “deficiency one algorithm” to such systems.

中文翻译：

---

幂律动力学系统多平稳性的计算方法

本文提出了一种计算解决方案，以确定具有幂律动力学的化学反应网络（PLK 系统）是否具有多平稳性，即是否存在正速率常数，使得相应的微分方程在一个范围内允许多个正稳态。化学计量类。该方法被称为“PLK 系统的多平稳算法”（MSA），它结合了（i）将 Ji 和 Feinberg 的质量作用的“更高缺陷算法”扩展到具有反应物确定相互作用的 PLK 系统，以及（ii） ) 一种将任何 PLK 系统转换为具有反应物确定相互作用的动态等效系统的方法。使用该算法，我们获得了两个新结果：一个流行的厌氧酵母发酵途径模型的单平稳性，以及具有气候工程的全球碳循环模型的多平稳性，均采用生化系统理论的广义质量作用格式。与 Feinberg 的“缺陷一算法”对此类系统的扩展相比，我们还提供了针对缺陷一 PLK 系统的更广泛方法的示例。