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Sibirskii Zhurnal Industrial'noi Matematiki, 2018, Volume 21, Number 1, Pages 47–60
DOI: https://doi.org/10.17377/sibjim.2018.21.105 (Mi sjim988) 		 
This article is cited in 2 scientific papers (total in 2 papers)

First integrals and periodic solutions of a system with power nonlinearities

A. A. Kosov, E. I. Semenov

Matrosov Institute for System Dynamics and Control Theory SB RAS, 134 Lermontov str., 664033 Irkutsk
Full-text PDF (314 kB) Citations (2)
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DOI: https://doi.org/10.17377/sibjim.2018.21.105
Abstract: Under consideration is some system of ordinary differential equations with power nonlinearities. These systems are widely used in mathematical biology and chemical kinetics, and can also occur by reduction of more sophisticated models. We formulate conditions on the system parameters which guarantee the existence of first integrals defined by the combinations of power and logarithmic functions of the phase variables. Using the first integrals, we construct periodic solutions for the three-variable systems. A few examples are given illustrating the results.
Keywords: system of ordinary differential equations, first integral, periodic solution, elliptic Jacobi function.
Funding agency Grant number
Russian Foundation for Basic Research 15-08-06680
Ministry of Education and Science of the Russian Federation НШ-8081.2016.9
Received: 17.04.2017
English version:
Journal of Applied and Industrial Mathematics, 2018, Volume 12, Issue 1, Pages 70–83
DOI: https://doi.org/10.1134/S1990478918010076
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: A. A. Kosov, E. I. Semenov, “First integrals and periodic solutions of a system with power nonlinearities”, Sib. Zh. Ind. Mat., 21:1 (2018), 47–60; J. Appl. Industr. Math., 12:1 (2018), 70–83
Citation in format AMSBIB
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\by A.~A.~Kosov, E.~I.~Semenov
\paper First integrals and periodic solutions of a~system with power nonlinearities
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 1
\pages 47--60
\mathnet{http://mi.mathnet.ru/sjim988}
\crossref{https://doi.org/10.17377/sibjim.2018.21.105}
\elib{https://elibrary.ru/item.asp?id=32872881}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 1
\pages 70--83
\crossref{https://doi.org/10.1134/S1990478918010076}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043280456}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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