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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 1, Pages 119–126 (Mi timm532)  

This article is cited in 7 scientific papers (total in 7 papers)

A direct method for calculating Lyapunov values of two-dimensional dynamical systems

G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova

Saint-Petersburg State University

Abstract: A direct method is proposed for studying the behavior of two-dimensional dynamical systems in the critical case when the linear part of the system has two purely imaginary eigenvalues. This method allows one to construct approximations to solutions of the system and to the “turn-round” time of the trajectory in the form of a finite series in powers of the initial datum. With the help of symbolic computations and the proposed method, first approximations of a solution are constructed and expressions for the first three Lyapunov quantities of the Liénard system are written.

Keywords: Lyapunov quantities, limit cycle, symbolic computations.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S119–S126

Bibliographic databases:

UDC: 517.977
Received: 04.03.2009

Citation: G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova, “A direct method for calculating Lyapunov values of two-dimensional dynamical systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 119–126; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S119–S126

Citation in format AMSBIB
\by G.~A.~Leonov, N.~V.~Kuznetsov, E.~V.~Kudryashova
\paper A direct method for calculating Lyapunov values of two-dimensional dynamical systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 119--126
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 272
\issue , suppl. 1
\pages S119--S126

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    This publication is cited in the following articles:
    1. Leonov G.A., Kuznetsov N.V., “Limit cycles of quadratic systems with a perturbed weak focus of order 3 and a saddle equilibrium at infinity”, Dokl. Math., 82:2 (2010), 693–696  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova, O. A. Kuznetsova, “Sovremennye metody simvolnykh vychislenii: lyapunovskie velichiny i 16-aya problema Gilberta”, Tr. SPIIRAN, 16 (2011), 5–36  mathnet
    3. 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”, Journal of Mathematical Sciences, 201:5 (2014), 645–662  mathnet  crossref  mathscinet
    4. Leonov G.A., Burova I.G., Aleksandrov K.D., “Visualization of Four Limit Cycles of Two-Dimensional Quadratic Systems in the Parameter Space”, Differ. Equ., 49:13 (2013), 1675–1703  crossref  mathscinet  zmath  isi  elib  scopus
    5. Leonov G.A., Kuznetsov N.V., “Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits”, Int. J. Bifurcation Chaos, 23:1 (2013), 1330002  crossref  mathscinet  zmath  isi  elib  scopus
    6. Czornik A., Jurgas P., “On the Lyapunov Exponents of Infinite-Dimensional Discrete Time-Varying Linear System”, 2016 21St International Conference on Methods and Models in Automation and Robotics (Mmar), IEEE, 2016, 496–499  crossref  isi  scopus
    7. N. I. Gusarova, S. A. Murtazina, M. F. Fazlytdinov, M. G. Yumagulov, “Operator methods for calculating Lyapunov values in problems on local bifurcations of dynamical systems”, Ufa Math. J., 10:1 (2018), 25–48  mathnet  crossref  isi  elib
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