TY - JOUR

T1 - Multiscale measures of phase-space trajectories

AU - Alberti, Tommaso

AU - Consolini, Giuseppe

AU - Ditlevsen, Peter D.

AU - Donner, Reik

AU - Quattrociocchi, Virgilio

PY - 2020/12/3

Y1 - 2020/12/3

N2 - 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 Henon 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 past5 x10 6 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.

AB - 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 Henon 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 past5 x10 6 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.

KW - EMPIRICAL MODE DECOMPOSITION

KW - POWER SPECTRA

KW - INTERMITTENCY

KW - SYNCHRONIZATION

KW - DIMENSION

KW - ENTROPY

KW - NUMBER

KW - NOISE

KW - AE

U2 - 10.1063/5.0008916

DO - 10.1063/5.0008916

M3 - Journal article

C2 - 33380062

VL - 30

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 12

M1 - 123116

ER -