Probing the phase space of coupled oscillators with Koopman analysis
- 14 September 2021
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 104 (3), 034211
- https://doi.org/10.1103/physreve.104.034211
Abstract
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.Funding Information
- National Natural Science Foundation of China (11775035)
- Fundamental Research Funds for the Central Universities (2019XD-A10)
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