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Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits

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Abstract

The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert’s sixteenth problem for quadratic systems, Aizerman’s problem, and Kalman’s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described.

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Authors and Affiliations

  1. St. Petersburg State University, Faculty of Mathematics and Mechanics, 28, Universitetky av., 198504, St. Petersburg, Russia

    G. A. Leonov & N. V. Kuznetsov

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

    N. V. Kuznetsov

Authors
  1. G. A. Leonov
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  2. N. V. Kuznetsov
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Correspondence to N. V. Kuznetsov.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 45, Proceedings of the Sixth International Conference on Differential and Functional Differential Equations and International Workshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 14–21 August, 2011). Part 1, 2012.

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Leonov, G.A., Kuznetsov, N.V. Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits. J Math Sci 201, 645–662 (2014). https://doi.org/10.1007/s10958-014-2017-6

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  • DOI: https://doi.org/10.1007/s10958-014-2017-6

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