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Siberian Journal of Pure and Applied Mathematics, 2016, Volume 16, Issue 4, Pages 28–37
DOI: https://doi.org/10.17377/PAM.2016.16.404 (Mi vngu419) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On one piecewise linear dynamical system which models a gene network with variable feedback

V. P. Golubyatnikovab, M. V. Kazantsevc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c Altai State Technical University
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DOI: https://doi.org/10.17377/PAM.2016.16.404
Abstract: Discretization of phase portrait of one 3-dimensional biochemical kinetics dynamical system with piecewise linear right-hand sides of special form is constructed. We describe geometry of this phase portrait and construct there a piecewise linear invariant surface bounded by a stable cycle which is composed by eight rectilinear segments.
Keywords: gene network modeling, positive and negative feedbacks, phase portraits of dynamical systems, cycles, invariant surfaces, the Poincare map, projective transformations.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00745_а
Received: 07.06.2016
English version:
Journal of Mathematical Sciences, 2018, Volume 230, Issue 1, Pages 46–54
DOI: https://doi.org/10.1007/s10958-018-3725-0
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: V. P. Golubyatnikov, M. V. Kazantsev, “On one piecewise linear dynamical system which models a gene network with variable feedback”, Sib. J. Pure and Appl. Math., 16:4 (2016), 28–37; J. Math. Sci., 230:1 (2018), 46–54
Citation in format AMSBIB
\Bibitem{GolKaz16}
\by V.~P.~Golubyatnikov, M.~V.~Kazantsev
\paper On one piecewise linear dynamical system which models a gene network with variable feedback
\jour Sib. J. Pure and Appl. Math.
\yr 2016
\vol 16
\issue 4
\pages 28--37
\mathnet{http://mi.mathnet.ru/vngu419}
\crossref{https://doi.org/10.17377/PAM.2016.16.404}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 230
\issue 1
\pages 46--54
\crossref{https://doi.org/10.1007/s10958-018-3725-0}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал чистой и прикладной математики
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