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Hidden attractor in smooth Chua systems. / Leonov, G. A.; Kuznetsov, N. V.; Vagaitsev, V. I.

In: Physica D: Nonlinear Phenomena, Vol. 241, No. 18, 15.09.2012, p. 1482-1486.

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

Harvard

Leonov, GA, Kuznetsov, NV & Vagaitsev, VI 2012, 'Hidden attractor in smooth Chua systems', Physica D: Nonlinear Phenomena, vol. 241, no. 18, pp. 1482-1486. https://doi.org/10.1016/j.physd.2012.05.016

APA

Leonov, G. A., Kuznetsov, N. V., & Vagaitsev, V. I. (2012). Hidden attractor in smooth Chua systems. Physica D: Nonlinear Phenomena, 241(18), 1482-1486. https://doi.org/10.1016/j.physd.2012.05.016

Vancouver

Leonov GA, Kuznetsov NV, Vagaitsev VI. Hidden attractor in smooth Chua systems. Physica D: Nonlinear Phenomena. 2012 Sep 15;241(18):1482-1486. https://doi.org/10.1016/j.physd.2012.05.016

Author

Leonov, G. A. ; Kuznetsov, N. V. ; Vagaitsev, V. I. / Hidden attractor in smooth Chua systems. In: Physica D: Nonlinear Phenomena. 2012 ; Vol. 241, No. 18. pp. 1482-1486.

BibTeX

@article{24871ac09e8541ffa8b1baaf75c7411e,
title = "Hidden attractor in smooth Chua systems",
abstract = "The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50-60s of the 20th century in automatic control systems with scalar piecewise-linear nonlinearity. This brings up the question about the excitation nature of hidden oscillations. In the present paper it is shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems. Here the possibility of the existence of a hidden chaotic attractor in a modified Chua's system with a smooth characteristic of nonlinear element is demonstrated.",
keywords = "Attractor localization, Hidden attractor, Hidden oscillation, Smooth Chua's system",
author = "Leonov, {G. A.} and Kuznetsov, {N. V.} and Vagaitsev, {V. I.}",
note = "Funding Information: This work was supported by the Academy of Finland , the Ministry of Education and Science (Russia) , Saint-Petersburg State University , and Russian Foundation for Basic Research .",
year = "2012",
month = sep,
day = "15",
doi = "10.1016/j.physd.2012.05.016",
language = "English",
volume = "241",
pages = "1482--1486",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "18",

}

RIS

TY - JOUR

T1 - Hidden attractor in smooth Chua systems

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

AU - Vagaitsev, V. I.

N1 - Funding Information: This work was supported by the Academy of Finland , the Ministry of Education and Science (Russia) , Saint-Petersburg State University , and Russian Foundation for Basic Research .

PY - 2012/9/15

Y1 - 2012/9/15

N2 - The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50-60s of the 20th century in automatic control systems with scalar piecewise-linear nonlinearity. This brings up the question about the excitation nature of hidden oscillations. In the present paper it is shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems. Here the possibility of the existence of a hidden chaotic attractor in a modified Chua's system with a smooth characteristic of nonlinear element is demonstrated.

AB - The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50-60s of the 20th century in automatic control systems with scalar piecewise-linear nonlinearity. This brings up the question about the excitation nature of hidden oscillations. In the present paper it is shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems. Here the possibility of the existence of a hidden chaotic attractor in a modified Chua's system with a smooth characteristic of nonlinear element is demonstrated.

KW - Attractor localization

KW - Hidden attractor

KW - Hidden oscillation

KW - Smooth Chua's system

UR - http://www.scopus.com/inward/record.url?scp=84864278119&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2012.05.016

DO - 10.1016/j.physd.2012.05.016

M3 - Article

VL - 241

SP - 1482

EP - 1486

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 18

ER -

ID: 5435431