标题： 基于几何奇摄动理论的化学反应网络的坐标无关模型降阶 显示英文标题

标题： Coordinate-independent model reductions of chemical reaction networks based on geometric singular perturbation theory

摘要： 准稳态近似（QSSA）是降低化学反应网络（CRN）复杂性的标准技术。任何基于QSSA的模型的有效性仅限于特定的参数范围，这些范围通常会重叠，意味着多个不同的简化模型可以同时有效。这种模糊性使分析变得不必要的复杂，因为选择适当的简化并不总是显而易见的。在这里，我们采用了一种更强大的替代方法：坐标无关的几何奇异摄动理论（ci-GSPT）结合参数化方法。该框架的一个关键优势是其能够推导出不依赖于变量中明显的时间尺度分离的简化模型，从而意味着更少限制的参数范围。我们在两个基准系统上展示了我们的方法。对于Michaelis-Menten（MM）反应，我们为特定参数配置的正常双曲且吸引的临界流形推导出唯一的模型简化。我们系统地探索了三个数量级的参数配置：渐近大、小和“阶一”。因此，我们提供了以下不同的模型简化：(i) 不可逆反应方案的14个相关参数配置和(ii) 可逆反应方案的25个参数配置（其他存在平凡简化或临界流形退化的参数配置简要讨论）。对于更复杂的Kim-Forger模型，我们提供了一种无需坐标变换的新简化，展示了该方法在更大系统中的适用性。 显示英文摘要

摘要： The quasi-steady-state approximation (QSSA) is a standard technique for reducing the complexity of chemical reaction networks (CRNs). The validity of any QSSA-based model is restricted to specific parameter regimes, which often overlap, meaning multiple different reduced models can be simultaneously valid. This ambiguity complicates unnecessarily the analysis, as selecting the appropriate reduction is not always straightforward. Here, we employ a more powerful alternative: coordinate-independent geometric singular perturbation theory (ci-GSPT) accompanied by the parametrization method. A key advantage of this framework is its ability to derive reduced models independent of a clear timescale separation in the variables which, in turn, means less-restricted parameter regimes. We demonstrate our approach on two benchmark systems. For the Michaelis-Menten (MM) reaction, we derive a unique model reduction for normally hyperbolic and attracting critical manifolds of a specific parameter configuration. We systematically explore parameter configurations across three orders of magnitude: asymptotically large, small, and `order one'. Hence, we provide distinct model reductions for: (i) 14 relevant parameter configurations of the irreversible reaction scheme and (ii) 25 for the reversible reaction scheme (other parameter configurations where there are trivial reductions or degeneracies in critical manifolds, are discussed briefly). For the more complex Kim-Forger model, we provide a new reduction without the need of a coordinate transformation showcasing the method's applicability to larger systems.