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Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems pp 5–13Cite as

Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 210))

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.

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, Saint Petersburg State University, Universitetski pr. 28, Saint-Petersburg, 198504, Russia

    Gennady A. Leonov

  2. Dept. of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, Agora, FIN-40014, Finland

    Nikolay V. Kuznetsov

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  1. Gennady A. Leonov
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  2. Nikolay V. Kuznetsov
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Correspondence to Gennady A. Leonov .

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Editors and Affiliations

  1. Faculty of Electrical Eng. & Comp. Sci, Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Ivan Zelinka

  2. , Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, China, People's Republic

    Guanrong Chen

  3. , Institute of Physical, University of Tuebingen, Auf der Morgenstelle 8, Tuebingen, 72076, Germany

    Otto E. Rössler

  4. Faculty of Electrical Eng. & Comp. Sci., Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Vaclav Snasel

  5. (MIR Labs), Scientific Network for Innovation, Machine Intelligence Research Labs, Auburn, 98071, Washington, USA

    Ajith Abraham

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Leonov, G.A., Kuznetsov, N.V. (2013). Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation. In: Zelinka, I., Chen, G., Rössler, O., Snasel, V., Abraham, A. (eds) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 210. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00542-3_3

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