期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 13, 期 4, 页码 1816-1846出版社
SIAM PUBLICATIONS
DOI: 10.1137/130943637
关键词
multiscale systems; slow-fast systems; transfer operator; Koopman operator
资金
- Australian Research Council [DP120104514]
This paper introduces coordinate-independent methods for analyzing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary dynamical system exhibits multiscale behavior and for estimating the time-scale separation. For systems with such behavior, we establish techniques for analyzing the fast dynamics in isolation, extracting slow variables for the system, and accurately simulating these slow variables at a large time step. We illustrate our method with numerical examples and show how the reduced slow dynamics faithfully represents statistical features of the full dynamics which are not coordinate dependent.
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