A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations (ODEs). In chemical reaction network theory, we are interested with connections between the structure of the CRN and qualitative properties of the corresponding ODEs. One of the results in decomposition theory of CRNs is that the intersection of the sets of positive steady states of the subsystems is equal to the set of positive steady states of the whole system, if the decomposition is independent. Hence, computational approach using independent decompositions can be used as an efficient tool in studying large systems. In this work, we provide a necessary and sufficient condition for the existence of a nontrivial independent decomposition of a CRN, which leads to a novel step-by-step method to obtain such decomposition, if it exists. We also illustrate these results using real-life examples. In particular, we show that a CRN of a popular model of anaerobic yeast fermentation pathway has a nontrivial independent decomposition, while a particular biological system, which is a metabolic network with one positive feedforward and a negative feedback has none. Finally, we analyze properties of positive steady states of reaction networks of specific influenza virus models.

化学反应网络 (CRN) 由反应组成，这些反应可以被视为存在于系统中的称为物种的实体之间的相互作用。由于具有动力学，CRN 具有相应的一组常微分方程 (ODE)。在化学反应网络理论中，我们对 CRN 的结构与相应 ODE 的定性性质之间的联系感兴趣。CRN 分解理论的一个结果是，如果分解是独立的，子系统的正稳态集的交集等于整个系统的正稳态集。因此，使用独立分解的计算方法可以用作研究大型系统的有效工具。在这项工作中，我们为 CRN 的非平凡独立分解的存在提供了必要和充分条件，这导致了一种新的逐步方法来获得这种分解，如果它存在的话。我们还使用现实生活中的例子来说明这些结果。特别是，我们展示了一种流行的厌氧酵母发酵途径模型的 CRN 具有非平凡的独立分解，而特定的生物系统，即具有一个正前馈和一个负反馈的代谢网络，则没有。最后，我们分析了特定流感病毒模型反应网络的正稳态特性。我们展示了一种流行的厌氧酵母发酵途径模型的 CRN 具有非平凡的独立分解，而特定的生物系统，即具有一个正前馈和一个负反馈的代谢网络，则没有。最后，我们分析了特定流感病毒模型反应网络的正稳态特性。我们展示了一种流行的厌氧酵母发酵途径模型的 CRN 具有非平凡的独立分解，而特定的生物系统，即具有一个正前馈和一个负反馈的代谢网络，则没有。最后，我们分析了特定流感病毒模型反应网络的正稳态特性。