Slow Invariant Manifolds of Slow–Fast Dynamical Systems

Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed 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, one hand, to propose a classification of most important them into two great categories: singular perturbation-based and curvature-based methods, other prove equivalence between any belonging same category categories. Then, deep analysis comparison each these enable state efficiency Flow Curvature Method is exemplified with paradigmatic Van der Pol system Lorenz slow-fast system.