Abstract
In this paper, we propose new approaches to the construction of extremely multistable systems containing one-, two-, and three-dimensional lattices of identical hidden chaotic attractors possessing the same Lyapunov exponents. In particular, we prove that for multidimensional models of automatic control systems in the Lurie form, it is always possible to pass from an interactive system to a cascade system; this substantially simplifies the procedure for constructing multidimensional lattices of identical chaotic attractors.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 168, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part I, 2019.
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Burkin, I.M., Kuznetsova, O.I. An Approach to Generating Extremely Multistable Chaotic Systems. J Math Sci 262, 779–789 (2022). https://doi.org/10.1007/s10958-022-05856-2
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DOI: https://doi.org/10.1007/s10958-022-05856-2
Keywords and phrases
- dynamical system
- chaos
- extreme multistability
- displacement of phase flow
- Lyapunov exponent
- Kaplan–Yorke dimension