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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, Volume 15, Issue 1, Pages 45–53 (Mi vngu361)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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


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English version:
Journal of Mathematical Sciences, 2016, 215:4, 475–483

UDC: 514.745.82
Received: 19.01.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Golubyatnikov, V. V. Ivanov, L. S. Minushkina, “O suschestvovanii tsikla v odnoi nesimmetrichnoi modeli koltsevoi gennoi seti”, Sib. zhurn. chist. i prikl. matem., 18:3 (2018), 27–35  mathnet  crossref
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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