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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 1, Pages 95–103
DOI: https://doi.org/10.33048/smzh.2022.63.106 (Mi smj7643) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On uniqueness of a cycle in one circular gene network model

V. P. Golubyatnikovab, L. S. Minushkinaa

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (279 kB) Citations (3)
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DOI: https://doi.org/10.33048/smzh.2022.63.106
Abstract: We obtain conditions for uniqueness of a cycle in the phase portrait of a piecewise linear dynamical system of the Elowitz–Leibler type which simulates the functioning of a simplest circular gene network. We describe the behavior of trajectories of this system in the invariant toric neighborhood of the cycle.
Keywords: circular gene network, positive and negative feedbacks, block-linear dynamical system, invariant domain, Poincaré map, fixed point, cycle.
Received: 18.01.2021
Revised: 25.06.2021
Accepted: 11.08.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 1, Pages 79–86
DOI: https://doi.org/10.1134/S0037446622010062
Bibliographic databases:
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: V. P. Golubyatnikov, L. S. Minushkina, “On uniqueness of a cycle in one circular gene network model”, Sibirsk. Mat. Zh., 63:1 (2022), 95–103; Siberian Math. J., 63:1 (2022), 79–86
Citation in format AMSBIB
\Bibitem{GolMin22}
\by V.~P.~Golubyatnikov, L.~S.~Minushkina
\paper On uniqueness of a~cycle in one circular gene network model
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 1
\pages 95--103
\mathnet{http://mi.mathnet.ru/smj7643}
\crossref{https://doi.org/10.33048/smzh.2022.63.106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4440267}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 1
\pages 79--86
\crossref{https://doi.org/10.1134/S0037446622010062}
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  • https://www.mathnet.ru/eng/smj7643
  • https://www.mathnet.ru/eng/smj/v63/i1/p95
    • This publication is cited in the following 3 articles:
    1. L. S. Minushkina, “Periodic Trajectories of Nonlinear Circular Gene Network Models”, Sib Math J, 65:3 (2024), 718  crossref
    2. L. S. Minushkina, “Periodicheskie traektorii nelineinykh modelei koltsevykh gennykh setei”, Vladikavk. matem. zhurn., 25:4 (2023), 80–90  mathnet  crossref
    3. V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina, “Stratifications and foliations in phase portraits of gene network models”, Vestn. VOGiS, 26:8 (2023), 758  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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