Slow–fast dynamical systems, i.e. singularly or nonsingularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating their equations. This paper aims, on the one hand, to propose a classification of the most important of them into two great categories: singular perturbation-based methods and curvature-based methods, and on the other hand, to prove the equivalence between any methods belonging to the same category and between the two categories. Then, a deep analysis and comparison between each of these methods enable to state the efficiency of the Flow Curvature Method which is exemplified with paradigmatic Van der Pol singularly perturbed dynamical system and Lorenz slow–fast dynamical system.

中文翻译：

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慢-快动力系统的慢不变量流形

慢-快动力系统，即奇异或非奇异摄动动力系统具有缓慢的不变流形，其轨迹在其上缓慢演化。自上个世纪以来，已经开发了各种方法来逼近他们的方程。一方面，本文旨在将其中最重要的方法分为两大类：基于奇异扰动的方法和基于曲率的方法，另一方面，证明属于以下类别的任何方法之间的等价性。同一类别和两个类别之间。然后，对这些方法中的每一种进行深入分析和比较，从而能够说明这些方法的效率。流动曲率法以范德波尔奇异摄动动力系统和洛伦兹慢-快动力系统为例。