In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism which describes several chemical reactions. In order to apply singular perturbation techniques, we determine an appropriate perturbation parameter \(\epsilon \) (which is related to the kinetic constants and initial conditions of the model), the inner and outer solutions and the matched expansions of the solutions, up to the first order in \(\epsilon \), in the total quasi-steady-state approximation (tQSSA) framework. The contribution of these expansions can be useful for the estimation of the kinetic parameters of the reaction by means of the interpolation of experimental data with the explicit approximations of the solutions. Some numerical results are discussed, showing the high reliability of the tQSSA with respect to the standard QSSA.

在本文中，我们研究了辅助（或偶联）反应的数学模型，该模型描述了几种化学反应。为了应用奇异摄动技术，我们确定适当的摄动参数\（\ epsilon \）（与模型的动力学常数和初始条件有关），内部和外部解以及解的匹配展开，向上到\（\ epsilon \）中的第一顺序，在总准稳态近似（tQSSA）框架中。这些扩展的贡献可通过使用实验数据与溶液的显式近似值进行插值来估计反应的动力学参数。讨论了一些数值结果，表明tQSSA相对于标准QSSA具有很高的可靠性。