论文标题
多个时间尺度和几何奇异扰动理论中的参数化方法
Multiple timescales and the parametrisation method in geometric singular perturbation theory
论文作者
论文摘要
我们提出了一种在几何奇异扰动问题中计算缓慢流形及其快速纤维束的新方法。这种与坐标无关的方法的灵感来自Cabré，Fontich和de la Llave引入的参数化方法。通过迭代求解所谓的共轭方程，我们的方法同时计算了慢速歧管和快速纤维束的参数化以及这些对象上的动力学，以任意高度的准确性。我们展示了这种自上而下的方法的力量，用于研究具有多个时间（即三个或更多时间）的系统。特别是，我们强调了隐藏时间尺度的出现，并展示了我们的方法如何揭示这些令人惊讶的多个时间尺度结构。我们还将参数化方法应用于几个反应网络问题。
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by the parametrisation method introduced by Cabré, Fontich and de la Llave. By iteratively solving a so-called conjugacy equation, our method simultaneously computes parametrisations of slow manifolds and fast fibre bundles, as well as the dynamics on these objects, to arbitrarily high degrees of accuracy. We show the power of this top-down method for the study of systems with multiple (i.e., three or more) timescales. In particular, we highlight the emergence of hidden timescales and show how our method can uncover these surprising multiple timescale structures. We also apply our parametrisation method to several reaction network problems.
