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Sib. J. Pure and Appl. Math., 2016, Volume 16, Issue 4, Pages 28–37 (Mi vngu419)  

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

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


DOI: https://doi.org/10.17377/PAM.2016.16.404

Full text: PDF file (283 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences, 2018, 230:1, 46–54

UDC: 514.745.82
Received: 07.06.2016

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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