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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 1, Pages 119–126
(Mi timm532)
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This article is cited in 17 scientific papers (total in 17 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.
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
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https://www.mathnet.ru/eng/timm532 https://www.mathnet.ru/eng/timm/v16/i1/p119
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Abstract page: | 851 | Full-text PDF : | 336 | References: | 59 | First page: | 15 |
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