研究多尺度系统中转变的数据驱动方法指南：李雅普诺夫向量的情况
Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors
摘要：
我们详细研究了协变李雅普诺夫向量和它们各自的角度检测亚稳态之间的转换动力系统，最近在几个大气科学应用中讨论的作用。基础模型是建立从数据的动态聚类方法，称为FEM-BV-VAR，和李雅普诺夫向量近似基于这些模型。我们测试这种基于数据的数值方法在三个很好理解的示例系统的手与动态复杂性的增加，确定关键的属性，允许成功应用的方法：特别是，事实证明，该方法需要一个明确的多时间尺度结构之间的快速过渡慢变子系统，可以动态的特点是不变的中性方向的线性逼近模型。
英文摘要：
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The underlying models are built from data by the dynamical clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated based on these models. We test this data-based numerical approach at the hand of three well-understood example systems with increasing dynamical complexity, identifying crucial properties that allow for a successful application of the method: in particular, it turns out that the method requires a clear multiple time scale structure with fast transitions between slow subsystems which can be dynamically characterized by invariant neutral directions of the linear approximation model.
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