https://doi.org/10.1140/epjb/s10051-024-00840-y
Regular Article - Statistical and Nonlinear Physics
Deciphering complexity: machine learning insights into the chaos
School of Physics, Free University of Tbilisi, David Aghmashenebeli Alley, 0159, Tbilisi, Georgia
a
lazare.osmanov1521r@gmail.com
Received:
13
August
2024
Accepted:
29
November
2024
Published online:
11
January
2025
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.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
