A computational method to extract macroscopic variables and their dynamics in multiscale systems

Gary Froyland, Georg Gottwald, Andrew Scott Hammerlindl

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33 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1816-1846
Number of pages31
JournalSIAM Journal on Applied Dynamical Systems
Issue number4
Publication statusPublished - 2014
Externally publishedYes

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