Sakata Itsushi, Kawahara Yoshinobu
RIKEN Center for Advanced Intelligence Project, Tokyo, Japan.
Graduate School of Information Science and Technology, Osaka University, Osaka, Japan.
Sci Rep. 2024 Aug 20;14(1):19276. doi: 10.1038/s41598-024-69837-y.
The analysis of complex behavior in empirical data poses significant challenges in various scientific and engineering disciplines. Dynamic Mode Decomposition (DMD) is a widely used method to reveal the spectral features of nonlinear dynamical systems without prior knowledge. However, because of its infinite dimensions, analyzing the continuous spectrum resulting from chaos and noise is problematic. We propose a clustering-based method to analyze dynamics represented by pseudoeigenfunctions associated with continuous spectra. This paper describes data-driven algorithms for comparing pseudoeigenfunctions using subspaces. We used the recently proposed Residual Dynamic Mode Decomposition (ResDMD) to approximate spectral properties from the data. To validate the effectiveness of our method, we analyzed 1D signal data affected by thermal noise and 2D-time series of coupled chaotic systems exhibiting generalized synchronization. The results reveal dynamic patterns previously obscured by conventional DMD analyses and provide insights into coupled chaos's complexities.
在各种科学和工程学科中，对经验数据中的复杂行为进行分析面临着重大挑战。动态模式分解（DMD）是一种广泛使用的方法，用于在无需先验知识的情况下揭示非线性动力系统的频谱特征。然而，由于其具有无限维度，分析由混沌和噪声产生的连续谱存在问题。我们提出一种基于聚类的方法来分析与连续谱相关的伪特征函数所表示的动力学。本文描述了使用子空间比较伪特征函数的数据驱动算法。我们使用最近提出的残差动态模式分解（ResDMD）从数据中近似频谱特性。为了验证我们方法的有效性，我们分析了受热噪声影响的一维信号数据以及表现出广义同步的耦合混沌系统的二维时间序列。结果揭示了先前传统DMD分析所掩盖的动态模式，并提供了对耦合混沌复杂性的见解。
