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Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator. / Kruglov, V. P.; Krylosova, D. A.; Sataev, I. R.; Seleznev, E. P.; Stankevich, N. V.

In: Chaos, Vol. 31, No. 7, 073118, 01.07.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Kruglov, VP, Krylosova, DA, Sataev, IR, Seleznev, EP & Stankevich, NV 2021, 'Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator', Chaos, vol. 31, no. 7, 073118. https://doi.org/10.1063/5.0055579

APA

Kruglov, V. P., Krylosova, D. A., Sataev, I. R., Seleznev, E. P., & Stankevich, N. V. (2021). Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator. Chaos, 31(7), [073118]. https://doi.org/10.1063/5.0055579

Vancouver

Kruglov VP, Krylosova DA, Sataev IR, Seleznev EP, Stankevich NV. Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator. Chaos. 2021 Jul 1;31(7). 073118. https://doi.org/10.1063/5.0055579

Author

Kruglov, V. P. ; Krylosova, D. A. ; Sataev, I. R. ; Seleznev, E. P. ; Stankevich, N. V. / Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator. In: Chaos. 2021 ; Vol. 31, No. 7.

BibTeX

@article{960583b256cc45e0990b35ca3ff21964,
title = "Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator",
abstract = "Transition to chaos via the destruction of a two-dimensional torus is studied numerically using an example of the H{\'e}non map and the Toda oscillator under quasiperiodic forcing and also experimentally using an example of a quasi-periodically excited RL-diode circuit. A feature of chaotic dynamics in these systems is the fact that the chaotic attractor in them has an additional zero Lyapunov exponent, which strictly follows from the structure of mathematical models. In the process of research, the influence of feedback is studied, in which the frequency of one of the harmonics of external forcing becomes dependent on a dynamic variable. Charts of dynamic regimes were constructed, examples of typical oscillation modes were given, and the spectrum of Lyapunov exponents was analyzed. Numerical simulations confirm that chaos resulting from the cascade of torus doubling has a close to the zero Lyapunov exponent, beside the trivial zero exponent.",
keywords = "BIFURCATIONS, TORUS, DESTRUCTION, SYSTEM",
author = "Kruglov, {V. P.} and Krylosova, {D. A.} and Sataev, {I. R.} and Seleznev, {E. P.} and Stankevich, {N. V.}",
note = "Publisher Copyright: {\textcopyright} 2021 Author(s).",
year = "2021",
month = jul,
day = "1",
doi = "10.1063/5.0055579",
language = "English",
volume = "31",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics",
number = "7",

}

RIS

TY - JOUR

T1 - Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator

AU - Kruglov, V. P.

AU - Krylosova, D. A.

AU - Sataev, I. R.

AU - Seleznev, E. P.

AU - Stankevich, N. V.

N1 - Publisher Copyright: © 2021 Author(s).

PY - 2021/7/1

Y1 - 2021/7/1

N2 - Transition to chaos via the destruction of a two-dimensional torus is studied numerically using an example of the Hénon map and the Toda oscillator under quasiperiodic forcing and also experimentally using an example of a quasi-periodically excited RL-diode circuit. A feature of chaotic dynamics in these systems is the fact that the chaotic attractor in them has an additional zero Lyapunov exponent, which strictly follows from the structure of mathematical models. In the process of research, the influence of feedback is studied, in which the frequency of one of the harmonics of external forcing becomes dependent on a dynamic variable. Charts of dynamic regimes were constructed, examples of typical oscillation modes were given, and the spectrum of Lyapunov exponents was analyzed. Numerical simulations confirm that chaos resulting from the cascade of torus doubling has a close to the zero Lyapunov exponent, beside the trivial zero exponent.

AB - Transition to chaos via the destruction of a two-dimensional torus is studied numerically using an example of the Hénon map and the Toda oscillator under quasiperiodic forcing and also experimentally using an example of a quasi-periodically excited RL-diode circuit. A feature of chaotic dynamics in these systems is the fact that the chaotic attractor in them has an additional zero Lyapunov exponent, which strictly follows from the structure of mathematical models. In the process of research, the influence of feedback is studied, in which the frequency of one of the harmonics of external forcing becomes dependent on a dynamic variable. Charts of dynamic regimes were constructed, examples of typical oscillation modes were given, and the spectrum of Lyapunov exponents was analyzed. Numerical simulations confirm that chaos resulting from the cascade of torus doubling has a close to the zero Lyapunov exponent, beside the trivial zero exponent.

KW - BIFURCATIONS

KW - TORUS

KW - DESTRUCTION

KW - SYSTEM

UR - http://www.scopus.com/inward/record.url?scp=85109632339&partnerID=8YFLogxK

U2 - 10.1063/5.0055579

DO - 10.1063/5.0055579

M3 - Article

C2 - 34340355

AN - SCOPUS:85109632339

VL - 31

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 7

M1 - 073118

ER -

ID: 86482483