Many physical phenomena in biology and physiology are described by mathematical models that comprise a system of initial value ordinary differential equations. Each differential equation may often be written as the sum of several terms, where each term represents a different physical entity. A wide range of techniques, ranging from heuristic observation to mathematically rigorous asymptotic analysis, may be used to simplify these equations allowing the identification of the key phenomena responsible for a given observed behaviour. In this study we extend an algorithm for automatically simplifying systems of initial value ordinary differential equations (Whiteley (2010)) that is based on a posteriori analysis of the full system of equations. Our extensions to the algorithm make the following contributions: (i) each equation in a system of differential equations may be written as a finite sum of contributions (including the derivative term), and any one of these terms may be neglected (if it is appropriate to do so) in the simplified model; and (ii) a simplified model is generated that allows accurate prediction of one or more components of the solution at all times. These extensions are illustrated using examples drawn from enzyme kinetics and cardiac electrophysiology.

生物学和生理学中的许多物理现象都是由数学模型描述的，这些数学模型包括初始值常微分方程组。每个微分方程通常可以写成几个项的总和，其中每个项代表一个不同的物理实体。可以使用从启发式观察到数学上严格的渐近分析的范围广泛的技术来简化这些方程，从而允许识别导致给定观察行为的关键现象。在这项研究中，我们扩展了一种算法，用于自动简化初始值常微分方程组 (Whiteley (2010))，该算法基于后验分析完整的方程组。我们对算法的扩展做出以下贡献：(i) 微分方程组中的每个方程都可以写成贡献的有限和（包括导数项），并且这些项中的任何一项都可以忽略（如果它是适合这样做）在简化模型中；(ii) 生成一个简化的模型，该模型允许始终准确预测解决方案的一个或多个组成部分。这些扩展使用来自酶动力学和心脏电生理学的例子来说明。