In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.

中文翻译：

---

一般化学反应系统中单射性和独特平衡的图论准则


在本文中，我们讨论了如何确定一般化学反应系统何时无法接受多重平衡的问题，无论反应速率常数等参数值如何，也无论化学动力学的类型（例如质量作用动力学）， Michaelis-Menten 动力学等。我们的结果与先前描述的化学反应系统的注入性的线性代数和图论条件相关。在两种形式之间进行转换后，我们表明，早期在具有质量作用动力学的系统背景下开发的图论测试可以应用于具有任意动力学的反应系统。该测试很容易通过算法实现，并且通常无需任何计算即可确定，排除了所讨论系统的多重平衡的可能性。