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A Comparison between four Chaotic Indicators in Systems with Hidden Attractors

Authors :
Maaita, Jamal-Odysseas
Prousalis, Dimitrios
Source :
Journal of Computational and Nonlinear Dynamics; 20240101, Issue: Preprints p1-13, 13p
Publication Year :
2024

Abstract

A non-regular oscillation is not enough to define a system as chaotic. A more in-depth investigation is required to prove the existence of chaotic behavior, which is challenging. Although many scientists use the Lyapunov Characteristic Exponents to detect chaos, it is not the only method. Several scientists have introduced different methods that utilize various properties of dynamical systems. The paper presents four different chaotic indicators based on the evolution of the deviation vectors: the maximal Lyapunov Exponent, the Lyapunov Characteristic Exponents, the Fast Lyapunov Index, and the Small Alignment Index. It includes their properties and the advantages and disadvantages of each method. Also, it includes the algorithms to calculate them and their implementation in Python. The paper closes with a comparison between the four indices applied to a system with hidden attractors.

Details

Language :
English
ISSN :
15551415 and 15551423
Issue :
Preprints
Database :
Supplemental Index
Journal :
Journal of Computational and Nonlinear Dynamics
Publication Type :
Periodical
Accession number :
ejs67795981
Full Text :
https://doi.org/10.1115/1.4067010