Probing the phase space of coupled oscillators with Koopman analysis,Physical Review E

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Probing the phase space of coupled oscillators with Koopman analysis
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-14 , DOI: 10.1103/physreve.104.034211
Shiyi Wang ₁ , Yueheng Lan _{1,

2}

Affiliation

With the development of probing and computing technology, the study of complex systems has become a necessity in various science and engineering problems, which may be treated efficiently with Koopman operator theory based on observed time series. In the current paper, combined with a singular value decomposition (SVD) of the constructed Hankel matrix, Koopman analysis is applied to a system of coupled oscillators. The spectral properties of the operator and the Koopman modes of a typical orbit reveal interesting invariant structures with periodic, quasiperiodic, or chaotic motion. By checking the amplitude of the principal modes along a straight line in the phase space, cusps of different sizes on the magnitude profiles are identified whenever a qualitative change of dynamics takes place. There seems to be no obstacle to extend the current analysis to high-dimensional nonlinear systems with intricate orbit structures.

中文翻译：

用 Koopman 分析探测耦合振荡器的相空间

随着探测技术和计算技术的发展，复杂系统的研究已成为各种科学和工程问题的必要条件，可以用基于观测时间序列的Koopman算子理论有效地处理这些问题。在当前的论文中，结合构建的 Hankel 矩阵的奇异值分解 (SVD)，将 Koopman 分析应用于耦合振荡器系统。算子的光谱特性和典型轨道的 Koopman 模式揭示了有趣的具有周期性、准周期性或混沌运动的不变结构。通过沿相空间中的一条直线检查主模式的幅度，每当发生动力学的质变时，就可以识别幅度分布上不同大小的尖点。

更新日期：2021-09-14

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