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  Multiscale measures of phase-space trajectories

Alberti, T., Consolini, G., Ditlevsen, P. D., Donner, R. V., Quattrociocchi, V. (2020): Multiscale measures of phase-space trajectories. - Chaos, 30, 12, 123116.
https://doi.org/10.1063/5.0008916

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 Creators:
Alberti, Tommaso1, Author
Consolini, Giuseppe1, Author
Ditlevsen, Peter D.1, Author
Donner, Reik V.2, Author              
Quattrociocchi, Virgilio1, Author
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1External Organizations, ou_persistent22              
2Potsdam Institute for Climate Impact Research, Potsdam, ou_persistent13              

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Free keywords: Thermodynamics; Topological properties; Henon map; Fractals; Nonlinear Geophysics; Lorenz system; Signal processing; Dynamical systems; Climate change; Space weather
 Abstract: Characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series is one of the most intensively studied contemporary problems in nonlinear sciences. In this work, we address this problem by combining two established concepts—empirical mode decomposition (EMD) and generalized fractal dimensions—into a unified analysis framework. Specifically, we demonstrate that the intrinsic mode functions derived by EMD can be used as a source of local (in terms of scales) information about the properties of the phase-space trajectory of the system under study, allowing us to derive multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three well-known low-dimensional deterministic dynamical systems (the Hénon map, the Lorenz ’63 system, and the standard map), three realizations of fractional Brownian motion with different Hurst exponents, and two somewhat higher-dimensional deterministic dynamical systems (the Lorenz ’96 model and the on–off intermittency model). These examples allow us to assess the performance of our formalism with respect to practically relevant aspects like additive noise, different initial conditions, the length of the time series under study, low- vs high-dimensional dynamics, and bursting effects. Finally, by taking advantage of two real-world systems whose multiscale features have been widely investigated (a marine stack record providing a proxy of the global ice volume variability of the past 5×10 6 5×106 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.

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 Dates: 2020-12-012020
 Publication Status: Finally published
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1063/5.0008916
MDB-ID: No data to archive
PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Research topic keyword: Nonlinear Dynamics
Research topic keyword: Complex Networks
Research topic keyword: Paleoclimate
Regional keyword: Global
Model / method: Nonlinear Data Analysis
Working Group: Development of advanced time series analysis techniques
 Degree: -

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Title: Chaos
Source Genre: Journal, SCI, Scopus, p3
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Pages: - Volume / Issue: 30 (12) Sequence Number: 123116 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/180808
Publisher: American Institute of Physics (AIP)