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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 4, Pages 69–76
DOI: https://doi.org/10.33048/SIBJIM.2020.23.405 (Mi sjim1109) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On invariant surfaces in gene network models

N. E. Kirillova

Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
Full-text PDF (531 kB) Citations (7)
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.405
Abstract: We construct an invariant two-dimensional surface in the phase portrait of a certain six-dimensional dynamical system which is considered as a model for the circular gene network functioning. This invariant surface contains an equilibrium point $S_0$ of the system, and if $S_0$ is hyperbolic then this surface contains a cycle of the system. The conditions for the existence of a cycle of this and similar systems were obtained earlier.
Keywords: circular gene network model, phase portrait, cycle, hyperbolic equilibrium point, invariant surface. .
Funding agency Grant number
Russian Foundation for Basic Research 20-31-90011
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1675
The author is grateful to N. B. Ayupova and V. P. Golubyatnikov for necessary recommendations and discussions, the anonymous reviewer for the helpful remarks, and V. N. Dyatlov for technical assistance.
Received: 12.06.2020
Revised: 09.08.2020
Accepted: 10.09.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 4, Pages 666–671
DOI: https://doi.org/10.1134/S1990478920040055
Bibliographic databases:
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: N. E. Kirillova, “On invariant surfaces in gene network models”, Sib. Zh. Ind. Mat., 23:4 (2020), 69–76; J. Appl. Industr. Math., 14:4 (2020), 666–671
Citation in format AMSBIB
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\by N.~E.~Kirillova
\paper On invariant surfaces in gene network models
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 4
\pages 69--76
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\crossref{https://doi.org/10.33048/SIBJIM.2020.23.405}
\elib{https://elibrary.ru/item.asp?id=44973479}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 4
\pages 666--671
\crossref{https://doi.org/10.1134/S1990478920040055}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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