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CMFD, 2012, Volume 45, Pages 105–121 (Mi cmfd216)  

Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits

G. A. Leonova, N. V. Kuznetsovab

a St. Petersburg State University, Faculty of Mathematics and Mechanics, St. Petersburg, Russia
b University of Jyväskylä, Department of Mathematical Information Technology, Jyväskylä, Finland

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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English version:
Journal of Mathematical Sciences, 2014, 201:5, 645–662

Bibliographic databases:

Document Type: Article
UDC: 531.36+534.1

Citation: G. A. Leonov, N. V. Kuznetsov, “Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, CMFD, 45, PFUR, M., 2012, 105–121; Journal of Mathematical Sciences, 201:5 (2014), 645–662

Citation in format AMSBIB
\Bibitem{LeoKuz12}
\by G.~A.~Leonov, N.~V.~Kuznetsov
\paper Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~1
\serial CMFD
\yr 2012
\vol 45
\pages 105--121
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd216}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3087054}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 201
\issue 5
\pages 645--662
\crossref{https://doi.org/10.1007/s10958-014-2017-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84905895534}


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