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Sibirskii Zhurnal Industrial'noi Matematiki, 2021, Volume 24, Number 3, Pages 19–29
DOI: https://doi.org/10.33048/SIBJIM.2021.24.302 (Mi sjim1139) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On stucture of phase portrait of one 5-dimensional gene network model

N. B. Ayupovaab, V. P. Golubyatnikovab

a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2021.24.302
Abstract: We obtain conditions of uniqueness of a cycle in phase portrait of one piecewise linear dynamical system which simulates functioning of a circular gene network with five components regulated by neagtive feedbacks only. We describe behavior of trajectories of this system in its invariant toric domain, and show stability of that cycle.
Keywords: circular gene network model, negative feedbacks, piecewise-linear dynamical systems, phase portrait, invariant domains, Poincaré mapping, monotonicity, fixed point, cycles, stability. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0011
The authors express their sincere gratitude to V. V. Ivanov, L. S. Minushkina, and V. N. Dyatlov for helpful discussions and critical comments.
Received: 10.03.2021
Revised: 19.04.2021
Accepted: 24.06.2021
English version:
Journal of Applied and Industrial Mathematics, 2021, Volume 15, Issue 3, Pages 376–383
DOI: https://doi.org/10.1134/S1990478921030029
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: N. B. Ayupova, V. P. Golubyatnikov, “On stucture of phase portrait of one 5-dimensional gene network model”, Sib. Zh. Ind. Mat., 24:3 (2021), 19–29; J. Appl. Industr. Math., 15:3 (2021), 376–383
Citation in format AMSBIB
\Bibitem{AyuGol21}
\by N.~B.~Ayupova, V.~P.~Golubyatnikov
\paper On stucture of phase portrait of one 5-dimensional gene network model
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 3
\pages 19--29
\mathnet{http://mi.mathnet.ru/sjim1139}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.302}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 3
\pages 376--383
\crossref{https://doi.org/10.1134/S1990478921030029}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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