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Scale dependence of fractal dimension in deterministic and stochastic Lorenz-63 systems

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posted on 2024-02-28, 15:49 authored by T Alberti, D Faranda, V Lucarini, RV Donner, B Dubrulle, F Daviaud
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of deterministic chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in the phase space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set. Indeed, it spans over a wide range of spatial scales and may even change in time due to non-stationary forcing. Here, we combine an adaptive decomposition method with extreme value theory to study the properties of the instantaneous scale-dependent dimension, which has been recently introduced to characterize such temporal and spatial scale-dependent attractors in turbulence and astrophysics. To provide a quantitative analysis of the properties of this metric, we test it on the well-known low-dimensional deterministic Lorenz-63 system perturbed with additive or multiplicative noise. We demonstrate that the properties of the invariant set depend on the scale we are focusing on and that the scale-dependent dimensions can discriminate between additive and multiplicative noise despite the fact that the two cases have exactly the same stationary invariant measure at large scales. The proposed formalism can be generally helpful to investigate the role of multi-scale fluctuations within complex systems, allowing us to deal with the problem of characterizing the role of stochastic fluctuations across a wide range of physical systems.

History

Author affiliation

College of Science & Engineering/Comp' & Math' Sciences

Version

  • AM (Accepted Manuscript)

Published in

Chaos

Volume

33

Issue

2

Pagination

023144

Publisher

AIP Publishing

issn

1054-1500

eissn

1089-7682

Copyright date

2023

Available date

2024-02-28

Spatial coverage

United States

Language

eng

Deposited by

Professor Valerio Lucarini

Deposit date

2024-02-26

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