Nonlinear Dynamics, volume 111, issue 6, pages 5859-5887
Hidden attractors in Chua circuit: mathematical theory meets physical experiments
Kuznetsov Nikolay V.
1, 2, 3
,
Mokaev Timur
3
,
Ponomarenko Vladimir
4
,
Seleznev Evgeniy
4
,
Stankevich Nataliya
4, 5
,
Chua Leon
6
4
6
Electrical Engineering Department, University of California, Berkeley, USA
|
Publication type: Journal Article
Publication date: 2022-12-21
Journal:
Nonlinear Dynamics
Quartile SCImago
Q1
Quartile WOS
Q1
Impact factor: 5.6
ISSN: 0924090X, 1573269X
Electrical and Electronic Engineering
Mechanical Engineering
Applied Mathematics
Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Abstract
After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaotic attractors of the considered dynamical models are rather artificial, computer-induced objects, i.e., they are generated not due to the physical nature of the process, but only by errors arising from the application of approximate numerical methods and finite-precision computations. Further justification for the possibility of a real existence of chaos in the study of a physical system developed in two directions. Within the first direction, effective analytic-numerical methods were invented providing the so-called computer-assisted proof of the existence of a chaotic attractor. In the framework of the second direction, attempts were made to detect chaotic behavior directly in a physical experiment, by designing a proper experimental setup. The first remarkable result in this direction is the experiment of L. Chua, in which he designed a simple RLC circuit (Chua circuit) containing a nonlinear element (Chua diode), and managed to demonstrate the real evidence of chaotic behavior in this circuit on the screen of oscilloscope. The mathematical model of the Chua circuit (further, Chua system) is also known to be the first example of a system in which the existence of a chaotic hidden attractor was discovered and the bifurcation scenario of its birth was described. Despite the nontriviality of this discovery and cogency of the procedure for hidden attractor localization, the question of detecting this type of attractor in a physical experiment remained open. This article aims to give an exhaustive answer to this question, demonstrating both a detailed formulation of a radiophysical experiment on the localization of a hidden attractor in the Chua circuit, as well as a thorough description of the relationship between a physical experiment, mathematical modeling, and computer simulation.
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- We do not take into account publications that without a DOI.
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- Statistics recalculated weekly.
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Kuznetsov N. V. et al. Hidden attractors in Chua circuit: mathematical theory meets physical experiments // Nonlinear Dynamics. 2022. Vol. 111. No. 6. pp. 5859-5887.
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Kuznetsov N. V., Mokaev T., Ponomarenko V., Seleznev E., Stankevich N., Chua L. Hidden attractors in Chua circuit: mathematical theory meets physical experiments // Nonlinear Dynamics. 2022. Vol. 111. No. 6. pp. 5859-5887.
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TY - JOUR
DO - 10.1007/s11071-022-08078-y
UR - https://doi.org/10.1007%2Fs11071-022-08078-y
TI - Hidden attractors in Chua circuit: mathematical theory meets physical experiments
T2 - Nonlinear Dynamics
AU - Kuznetsov, Nikolay V.
AU - Mokaev, Timur
AU - Ponomarenko, Vladimir
AU - Seleznev, Evgeniy
AU - Stankevich, Nataliya
AU - Chua, Leon
PY - 2022
DA - 2022/12/21 00:00:00
PB - Springer Nature
SP - 5859-5887
IS - 6
VL - 111
SN - 0924-090X
SN - 1573-269X
ER -
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@article{2022_Kuznetsov,
author = {Nikolay V. Kuznetsov and Timur Mokaev and Vladimir Ponomarenko and Evgeniy Seleznev and Nataliya Stankevich and Leon Chua},
title = {Hidden attractors in Chua circuit: mathematical theory meets physical experiments},
journal = {Nonlinear Dynamics},
year = {2022},
volume = {111},
publisher = {Springer Nature},
month = {dec},
url = {https://doi.org/10.1007%2Fs11071-022-08078-y},
number = {6},
pages = {5859--5887},
doi = {10.1007/s11071-022-08078-y}
}
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Kuznetsov, Nikolay V., et al. “Hidden attractors in Chua circuit: mathematical theory meets physical experiments.” Nonlinear Dynamics, vol. 111, no. 6, Dec. 2022, pp. 5859-5887. https://doi.org/10.1007%2Fs11071-022-08078-y.
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