Hidden attractors in Chua circuit : mathematical theory meets physical experiments
Kuznetsov, N., Mokaev, T., Ponomarenko, V., Seleznev, E., Stankevich, N., & Chua, L. (2023). Hidden attractors in Chua circuit : mathematical theory meets physical experiments. Nonlinear Dynamics, 111(6), 5859-5887. https://doi.org/10.1007/s11071-022-08078-y
Published inNonlinear Dynamics
DisciplineLaskennallinen tiedeComputing, Information Technology and MathematicsComputational ScienceComputing, Information Technology and Mathematics
© The Author(s) 2022
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. ...
PublisherSpringer Science and Business Media LLC
ISSN Search the Publication Forum0924-090X
Publication in research information system
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Additional information about fundingOpen Access funding provided by the University of Jyväskylä. (JYU). The work is carried out with the financial support of the Russian Science Foundation (22-11-00172) [section 1,5], Leading Scientific Schools program (project NSh-4196.1.1) and St.Petersburg State University grant (Pure ID 75207094). Experiments and technique of visualization of hidden attractor and multistability were implemented at Kotelnikov’s Institute of Radio-electronics and Engineering RAS (Saratov branch) with financial support of the Russian Science Foundation (grant No. 21-12-00121) [section 4]. ...
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