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Deciphering complexity: machine learning insights into the chaos.

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Title: Deciphering complexity: machine learning insights into the chaos.
Authors: Osmanov, Lazare1 (AUTHOR) lazare.osmanov1521r@gmail.com
Source: European Physical Journal B: Condensed Matter. Jan2025, Vol. 98 Issue 1, p1-10. 10p.
Subjects: Conserved quantity, Dynamical systems, Phase transitions, Integers, Lyapunov exponents
Abstract: We introduce new machine learning techniques for analyzing chaotic dynamical systems. The main goal of this study is to develop a simple method for calculating the Lyapunov exponent using only two trajectory data points, in contrast to traditional methods that require averaging procedures. Additionally, we explore phase transition graphs to analyze the shift from regular periodic to chaotic dynamics, focusing on identifying "almost integrable" trajectories where conserved quantities deviate from whole numbers. Furthermore, we identify "integrable regions" within chaotic trajectories. These methods are tested on two dynamical systems: "two objects moving on a rod" and the "Henon–Heiles" system. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal B: Condensed Matter is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Deciphering complexity: machine learning insights into the chaos.
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  Data: We introduce new machine learning techniques for analyzing chaotic dynamical systems. The main goal of this study is to develop a simple method for calculating the Lyapunov exponent using only two trajectory data points, in contrast to traditional methods that require averaging procedures. Additionally, we explore phase transition graphs to analyze the shift from regular periodic to chaotic dynamics, focusing on identifying "almost integrable" trajectories where conserved quantities deviate from whole numbers. Furthermore, we identify "integrable regions" within chaotic trajectories. These methods are tested on two dynamical systems: "two objects moving on a rod" and the "Henon–Heiles" system. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of European Physical Journal B: Condensed Matter is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1140/epjb/s10051-024-00840-y
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      – Code: eng
        Text: English
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      – SubjectFull: Conserved quantity
        Type: general
      – SubjectFull: Dynamical systems
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      – SubjectFull: Phase transitions
        Type: general
      – SubjectFull: Integers
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      – SubjectFull: Lyapunov exponents
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      – TitleFull: Deciphering complexity: machine learning insights into the chaos.
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            – D: 01
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              Text: Jan2025
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              Y: 2025
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