论文标题
缓慢快速动力学系统的慢速流形
Slow Invariant Manifolds of Slow-Fast Dynamical Systems
论文作者
论文摘要
缓慢快速的动态系统，即单一或非扰动的动力学系统具有缓慢的轨迹在其上缓慢发展的慢速歧管。自上世纪以来，已经开发了各种方法来近似其方程。一方面，本文的目的是将其中最重要的分类分为两个大类：基于奇异扰动的方法和基于曲率的方法，另一方面，以证明属于同一类别的任何方法与这两个类别之间的任何方法之间的等效性。然后，这些方法中的每种方法之间进行了深入的分析和比较，以说明流动曲率方法的效率，该方法用范式范围的范围倾斜的动力学系统和洛伦兹慢速动力学系统进行了例证。
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.
