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Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems : Analytics and Simulation. / Leonov, Gennady A.; Kuznetsov, Nikolay V.

Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Springer Nature, 2013. p. 5-13 (Advances in Intelligent Systems and Computing; Vol. 210).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Leonov, GA & Kuznetsov, NV 2013, Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation. in Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol. 210, Springer Nature, pp. 5-13. https://doi.org/10.1007/978-3-319-00542-3_3, https://doi.org/10.1007/978-3-319-00542-3_3

APA

Leonov, G. A., & Kuznetsov, N. V. (2013). Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation. In Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems (pp. 5-13). (Advances in Intelligent Systems and Computing; Vol. 210). Springer Nature. https://doi.org/10.1007/978-3-319-00542-3_3, https://doi.org/10.1007/978-3-319-00542-3_3

Vancouver

Leonov GA, Kuznetsov NV. Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation. In Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Springer Nature. 2013. p. 5-13. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-319-00542-3_3, https://doi.org/10.1007/978-3-319-00542-3_3

Author

Leonov, Gennady A. ; Kuznetsov, Nikolay V. / Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems : Analytics and Simulation. Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Springer Nature, 2013. pp. 5-13 (Advances in Intelligent Systems and Computing).

BibTeX

@inbook{01a7f99abb8c47128c08e844875b8e74,
title = "Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation",
abstract = "From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. This keynote lecture is devoted to affective analytical-numerical methods for localization of hidden oscillations in nonlinear dynamical systems and their application to well known fundamental problems and applied models.",
author = "Leonov, {Gennady A.} and Kuznetsov, {Nikolay V.}",
year = "2013",
doi = "10.1007/978-3-319-00542-3_3",
language = "English",
isbn = "9783319005416",
series = "Advances in Intelligent Systems and Computing",
publisher = "Springer Nature",
pages = "5--13",
booktitle = "Nostradamus 2013",
address = "Germany",

}

RIS

TY - CHAP

T1 - Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems

T2 - Analytics and Simulation

AU - Leonov, Gennady A.

AU - Kuznetsov, Nikolay V.

PY - 2013

Y1 - 2013

N2 - From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. This keynote lecture is devoted to affective analytical-numerical methods for localization of hidden oscillations in nonlinear dynamical systems and their application to well known fundamental problems and applied models.

AB - From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. This keynote lecture is devoted to affective analytical-numerical methods for localization of hidden oscillations in nonlinear dynamical systems and their application to well known fundamental problems and applied models.

UR - http://www.scopus.com/inward/record.url?scp=84880353943&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-00542-3_3

DO - 10.1007/978-3-319-00542-3_3

M3 - Chapter

SN - 9783319005416

T3 - Advances in Intelligent Systems and Computing

SP - 5

EP - 13

BT - Nostradamus 2013

PB - Springer Nature

ER -

ID: 4703877