Siberian Journal of Pure and Applied Mathematics
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Siberian Journal of Pure and Applied Mathematics, 2018, Volume 18, Issue 1, Pages 54–63
DOI: https://doi.org/10.17377/PAM.2018.18.5 (Mi vngu463) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On cycles in models of functioning of circular gene networks

V. P. Golubyatnikovab, N. E. Kirillovab

a Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk 630090, Russia
b Novosibirsk State University, 1, Pirogova St., Novosibirsk 630090, Russia
Full-text PDF (722 kB) Citations (9)
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DOI: https://doi.org/10.17377/PAM.2018.18.5
Abstract: We study a phase portrait of a nonlinear 10-dimensional dynamical system describing a model of functioning of one circular gene network. We find sufficient conditions for the existence of a cycle in this phase portrait. For a similar 18-dimensional dynamical system, we find conditions for the existence of at least two cycles in its phase portrait.
Keywords: nonlinear dynamical systems, circular gene network, phase portraits, cycles, torus principle.
Received: 29.05.2017
English version:
Journal of Mathematical Sciences, 2020, Volume 246, Issue 6, Pages 779–787
DOI: https://doi.org/10.1007/s10958-020-04780-7
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: V. P. Golubyatnikov, N. E. Kirillova, “On cycles in models of functioning of circular gene networks”, Sib. J. Pure and Appl. Math., 18:1 (2018), 54–63; J. Math. Sci., 246:6 (2020), 779–787
Citation in format AMSBIB
\Bibitem{GolKir18}
\by V.~P.~Golubyatnikov, N.~E.~Kirillova
\paper On cycles in models of functioning of circular gene networks
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 1
\pages 54--63
\mathnet{http://mi.mathnet.ru/vngu463}
\crossref{https://doi.org/10.17377/PAM.2018.18.5}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 246
\issue 6
\pages 779--787
\crossref{https://doi.org/10.1007/s10958-020-04780-7}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал чистой и прикладной математики
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