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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2015, Volume 15, Issue 1, Pages 45–53 (Mi vngu361)  
This article is cited in 2 scientific papers (total in 2 papers)

On structure of phase portraits of some nonlinear dynamical systems

V. P. Golubyatnikovab, A. E. Kalenykhb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (335 kB) Citations (2)
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Abstract: We study phase portrait of one piece-wise linear dynamical system of chemical kinetics. Earlier L. Glass and J. Pasternack have obtained conditions of existence of a stable cycle of this system. We construct here an invariant piece-wise linear surface which consists of trajectories of this system and is disjoined with the attraction basin of that stable cycle. We prove that this surface does not contain cycles of this dynamical system.
Keywords: dynamical systems, phase portraits, oscillating trajectories, invariant surfaces.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00745
Received: 19.01.2015
English version:
Journal of Mathematical Sciences, 2016, Volume 215, Issue 4, Pages 475–483
DOI: https://doi.org/10.1007/s10958-016-2852-8
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:1 (2015), 45–53; J. Math. Sci., 215:4 (2016), 475–483
Citation in format AMSBIB
\Bibitem{GolKal15}
\by V.~P.~Golubyatnikov, A.~E.~Kalenykh
\paper On structure of phase portraits of some nonlinear dynamical systems
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2015
\vol 15
\issue 1
\pages 45--53
\mathnet{http://mi.mathnet.ru/vngu361}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 215
\issue 4
\pages 475--483
\crossref{https://doi.org/10.1007/s10958-016-2852-8}
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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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    		Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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