Standard

Hidden oscillations in dynamical systems. / Leonov, G. A.; Kuznetsov, N. V.; Kuznetsova, O. A.; Seledzhi, S. M.; Vagaitsev, V. I.

In: WSEAS Transactions on Systems and Control, Vol. 6, No. 2, 02.2011, p. 54-67.

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

Harvard

Leonov, GA, Kuznetsov, NV, Kuznetsova, OA, Seledzhi, SM & Vagaitsev, VI 2011, 'Hidden oscillations in dynamical systems', WSEAS Transactions on Systems and Control, vol. 6, no. 2, pp. 54-67.

APA

Leonov, G. A., Kuznetsov, N. V., Kuznetsova, O. A., Seledzhi, S. M., & Vagaitsev, V. I. (2011). Hidden oscillations in dynamical systems. WSEAS Transactions on Systems and Control, 6(2), 54-67.

Vancouver

Leonov GA, Kuznetsov NV, Kuznetsova OA, Seledzhi SM, Vagaitsev VI. Hidden oscillations in dynamical systems. WSEAS Transactions on Systems and Control. 2011 Feb;6(2):54-67.

Author

Leonov, G. A. ; Kuznetsov, N. V. ; Kuznetsova, O. A. ; Seledzhi, S. M. ; Vagaitsev, V. I. / Hidden oscillations in dynamical systems. In: WSEAS Transactions on Systems and Control. 2011 ; Vol. 6, No. 2. pp. 54-67.

BibTeX

@article{8a208ddb7a054d1085754370a5ef334b,
title = "Hidden oscillations in dynamical systems",
abstract = "The classical attractors of Lorenz, R{\"o}ssler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use standard numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. Study of hidden oscillations and attractors requires the development of new analytical and numerical methods which will be considered in this paper.",
keywords = "Aizerman conjecture, Attractor localization, Describing function method, Harmonic balance, Hidden attractor, Hidden oscillation, Hilbert 16th problem, Kalman conjecture",
author = "Leonov, {G. A.} and Kuznetsov, {N. V.} and Kuznetsova, {O. A.} and Seledzhi, {S. M.} and Vagaitsev, {V. I.}",
year = "2011",
month = feb,
language = "English",
volume = "6",
pages = "54--67",
journal = "WSEAS Transaction on Systems and Control",
issn = "1991-8763",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "2",

}

RIS

TY - JOUR

T1 - Hidden oscillations in dynamical systems

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

AU - Kuznetsova, O. A.

AU - Seledzhi, S. M.

AU - Vagaitsev, V. I.

PY - 2011/2

Y1 - 2011/2

N2 - The classical attractors of Lorenz, Rössler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use standard numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. Study of hidden oscillations and attractors requires the development of new analytical and numerical methods which will be considered in this paper.

AB - The classical attractors of Lorenz, Rössler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use standard numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. Study of hidden oscillations and attractors requires the development of new analytical and numerical methods which will be considered in this paper.

KW - Aizerman conjecture

KW - Attractor localization

KW - Describing function method

KW - Harmonic balance

KW - Hidden attractor

KW - Hidden oscillation

KW - Hilbert 16th problem

KW - Kalman conjecture

UR - http://www.scopus.com/inward/record.url?scp=80053159371&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80053159371

VL - 6

SP - 54

EP - 67

JO - WSEAS Transaction on Systems and Control

JF - WSEAS Transaction on Systems and Control

SN - 1991-8763

IS - 2

ER -

ID: 95274678