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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 2, Pages 123–133
DOI: https://doi.org/10.1134/S1560354715020021 (Mi rcd49) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Analytical Solutions of the Lorenz System

Nikolay A. Kudryashov

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Shosse 31, Moscow, 115409 Russia
Citations (14)
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DOI: https://doi.org/10.1134/S1560354715020021
Abstract: The Lorenz system is considered. The Painlevé test for the third-order equation corresponding to the Lorenz model at $\sigma \ne 0$ is presented. The integrable cases of the Lorenz system and the first integrals for the Lorenz system are discussed. The main result of the work is the classification of the elliptic solutions expressed via the Weierstrass function. It is shown that most of the elliptic solutions are degenerated and expressed via the trigonometric functions. However, two solutions of the Lorenz system can be expressed via the elliptic functions.
Keywords: Lorenz system, Painlevé property, Painlevé test, analytical solutions, elliptic solutions.
Funding agency Grant number
Russian Science Foundation 14-11-00258
This research was supported by the Russian Science Foundation grant No. 14-11-00258.
Received: 08.01.2015
Bibliographic databases:
Document Type: Article
MSC: 01-00, 01A55, 01A60
Language: English
Citation: Nikolay A. Kudryashov, “Analytical Solutions of the Lorenz System”, Regul. Chaotic Dyn., 20:2 (2015), 123–133
Citation in format AMSBIB
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\by Nikolay A. Kudryashov
\paper Analytical Solutions of the Lorenz System
\jour Regul. Chaotic Dyn.
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\vol 20
\issue 2
\pages 123--133
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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