Quality Evaluation for Reconstructing Chaotic Attractors

Frunzete, Madalin

doi:10.3390/math10224229

Cited by 3 publications

(1 citation statement)

References 33 publications

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“…A remarkable consequence of the chaotic systems is that phase space presents strange attractors, characterized by fractal measures [59,62]. The Lorenz fractal is a very popular example derived from simplified Navier-Stokes equations [63].…”

Section: Geometry In Dynamical Systemsmentioning

confidence: 99%

Review: Fractal Geometry in Precipitation

Monjo,

Meseguer-Ruiz

2024

Atmosphere

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Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cycle, among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal indices, that is, non-integer values that represent the complexity of variables like the rainfall. However, observed precipitation is measured as an aggregate variable over time; thus, a physical analysis of observed fluxes is very limited. Consequently, this review aims to go through the different approaches used to identify and analyze the complexity of observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for the classification of climatic features, including the monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy, and time-scaling in intensity–duration–frequency curves.

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Section: Geometry In Dynamical Systemsmentioning

confidence: 99%

Review: Fractal Geometry in Precipitation

Monjo,

Meseguer-Ruiz

2024

Atmosphere

View full text Add to dashboard Cite

show abstract

Review: Fractal Geometry in Precipitation

Monjo,

Meseguer-Ruiz

2024

Preprint

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Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, represented by a set of physical equations such as the Navier-Stokes equations, energy balances and hydrological cycle among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal dimensions, which are non-integer values that represent the complexity of variables like the precipitation. However, observed precipitation is measured as an aggregate variable over time, thus physical analysis of the observed fluxes is very limited. Therefore, this review aims to go through the different approaches used in the identification and analysis of the complexity of the observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for classification of climatic features, including monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy and time scaling in intensity-duration-frequency curves.

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Singularity, Observability and Statistical Independence in the Context of Chaotic Systems

Dinu

Frunzete

2023

Mathematics

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Pseudorandom number generators (PRNGs) have always been a central research topic in data science, and chaotic dynamical systems are one of the means to obtain scientifically proven data. Chaotic dynamical systems have the property that they have a seemingly unpredictable and random behavior obtained by making use of deterministic laws. The current paper will show how several notions used in the study of chaotic systems—statistical independence, singularity, and observability—can be used together as a suite of test methods for chaotic systems with high potential of being used in the PRNG or cryptography fields. In order to address these topics, we relied on the adaptation of the observability coefficient used in previous papers of the authors, we calculated the singularity areas for the chaotic systems considered, and we evaluated the selected chaotic maps from a statistical independence point of view. By making use of the three notions above, we managed to find strong correlations between the methods proposed, thus supporting the idea that the resulting test procedure is consistent. Future research directions consist of applying the proposed test procedure to other chaotic systems in order to gather more data and formalize the approach in a test suite that can be used by the data scientist when selecting the best chaotic system for a specific use (PRNG, cryptography, etc.).

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Quality Evaluation for Reconstructing Chaotic Attractors

Cited by 3 publications

References 33 publications

Review: Fractal Geometry in Precipitation

Review: Fractal Geometry in Precipitation

Review: Fractal Geometry in Precipitation

Singularity, Observability and Statistical Independence in the Context of Chaotic Systems

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