A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Hidden attractors in Chua circuit : mathematical theory meets physical experiments (2023)

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

JYU-tekijät tai -toimittajat

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Kuznetsov, Nikolay; Mokaev, Timur; Ponomarenko, Vladimir; Seleznev, Evgeniy; Stankevich, Nataliya; Chua, Leon

Lehti tai sarja: Nonlinear Dynamics

ISSN: 0924-090X

eISSN: 1573-269X

Julkaisuvuosi: 2023

Ilmestymispäivä: 21.12.2022

Volyymi: 111

Lehden numero: 6

Artikkelin sivunumerot: 5859-5887

Kustantaja: Springer Science and Business Media LLC

Julkaisumaa: Alankomaat

Julkaisun kieli: englanti

DOI: https://doi.org/10.1007/s11071-022-08078-y

Julkaisun avoin saatavuus: Avoimesti saatavilla

Julkaisukanavan avoin saatavuus: Osittain avoin julkaisukanava

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/84765

Tiivistelmä

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.

YSO-asiasanat: elektroniset piirit; fysikaaliset ilmiöt; matemaattiset mallit; dynaamiset systeemit; kaaosteoria; attraktorit

Vapaat asiasanat: hidden attractors; bifurcations; radiophysical experiment; Chua circuit

Liittyvät organisaatiot

OKM-raportointi: Kyllä

VIRTA-lähetysvuosi: 2023

JUFO-taso: 2