We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast variables are made, or necessary. We apply the theoretical results to chemical reaction networks with mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems, there exist canonical parameterizations of the variety of stationary points; hence, the theory is applicable in a natural manner. In particular, we obtain a closed form expression for the reduced system when the fast subsystem admits complex-balanced steady states.

中文翻译：

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Tikhonov–Fenichel简化的参数化临界流形及其在化学反应网络中的应用

我们推导了具有已知临界流形参数化的奇摄动常微分方程（在Tikhonov和Fenichel的意义上）的简化公式。没有做出关于慢速和快速变量分离的先验假设，也没有必要。我们将理论结果应用到具有质量动力学的化学反应网络中，从而允许缓慢和快速的反应。对于此类系统的某些相关类别，存在各种固定点的规范参数化；因此，该理论自然适用。特别是，当快速子系统接受复平衡稳态时，我们获得了简化系统的闭式表达式。