We investigate various estimators based on extreme value theory (EVT) for determining the local fractal dimension of chaotic dynamical systems. In the limit of an infinitely long time series of an ergodic system, the average of the local fractal dimension is the system’s global attractor dimension. The latter is an important quantity that relates to the number of effective degrees of freedom of the underlying dynamical system, and its estimation has been a central topic in the dynamical systems literature since the 1980s. In this work, we propose a framework that combines phase space recurrence analysis with EVT to estimate the local fractal dimension around a particular state of interest. While the EVT framework allows for the analysis of high-dimensional complex systems, such as the Earth’s climate, its effectiveness depends on robust statistical parameter estimation for the assumed extreme value distribution. In this study, we conduct a critical review of several EVT-based local fractal dimension estimators, analyzing and comparing their performance across a range of systems. Our results offer valuable insights for researchers employing the EVT-based estimates of the local fractal dimension, aiding in the selection of an appropriate estimator for their specific applications.
Skip Nav Destination
,
,
Article navigation
July 2023
Research Article|
July 19 2023
Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems Available to Purchase
Flavio Pons
;
Flavio Pons
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft)
1
LSCE-IPSL, CEA Saclay l’Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay
, 91191 Gif-sur-Yvette, France
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Gabriele Messori
;
Gabriele Messori
b)
(Conceptualization, Methodology, Writing – original draft)
2
Department of Earth Sciences and Centre of Natural Hazards and Disaster Science (CNDS), Uppsala University
, Uppsala 752 36, Sweden
Search for other works by this author on:
Davide Faranda
Davide Faranda
c)
(Conceptualization, Investigation, Writing – original draft)
1
LSCE-IPSL, CEA Saclay l’Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay
, 91191 Gif-sur-Yvette, France
Search for other works by this author on:
Flavio Pons
1,a)
Gabriele Messori
2,b)
Davide Faranda
1,c)
1
LSCE-IPSL, CEA Saclay l’Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay
, 91191 Gif-sur-Yvette, France
2
Department of Earth Sciences and Centre of Natural Hazards and Disaster Science (CNDS), Uppsala University
, Uppsala 752 36, Sweden
a)Author to whom correspondence should be addressed: [email protected]
b)
Also at: Department of Meteorology and Bolin Centre for Climate Research, Stockholm University, 106 91 Stockholm, Sweden.
c)
Also at: London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, UK.
Chaos 33, 073143 (2023)
Article history
Received:
March 29 2023
Accepted:
June 28 2023
Citation
Flavio Pons, Gabriele Messori, Davide Faranda; Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems. Chaos 1 July 2023; 33 (7): 073143. https://doi.org/10.1063/5.0152370
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto–Sivashinsky test case
Rambod Mojgani, Ashesh Chattopadhyay, et al.
Enhancing reservoir predictions of chaotic time series by incorporating delayed values of input and reservoir variables
Luk Fleddermann, Sebastian Herzog, et al.
Recent achievements in nonlinear dynamics, synchronization, and networks
Dibakar Ghosh, Norbert Marwan, et al.
Related Content
Limitations of estimating local dimension and extremal index using exceedances in dynamical systems
Chaos (April 2025)
Semiclassical mechanics of bound chaotic potentials
Chaos (January 1992)
Dynamical footprints of hurricanes in the tropical dynamics
Chaos (January 2023)
On removing the classical-quantum boundary
AIP Advances (October 2024)