  Slow-fast dynamical systems, i.e., singularly or non-singularly 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.
