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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 3, Pages 39–47
DOI: https://doi.org/10.33048/sibjim.2019.22.304 (Mi sjim1052) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Monotonicity of the Poincaré mapping in some models of circular gene networks

V. P. Golubyatnikovab, L. S. Minushkinab

a Sobolev Institute of Mathematics SB RAS pr. Akad. Koptyuga 4, 630090 Novosibirsk
b Novosibirsk State University, ul. Pirogova 1, 630090 Novosibirsk
Full-text PDF (221 kB) Citations (8)
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DOI: https://doi.org/10.33048/sibjim.2019.22.304
Abstract: We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz–Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.
Keywords: circular gene network, positive and negative feedbacks, piecewise-linear dynamical system, invariant domain, Poincaré mapping, cycle.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00057_a
Siberian Branch of Russian Academy of Sciences I.1.5 (проект 0314-2018-0011)
Received: 29.11.2018
Revised: 16.04.2019
Accepted: 13.06.2019
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 3, Pages 472–479
DOI: https://doi.org/10.1134/S1990478919030086
Bibliographic databases:
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: V. P. Golubyatnikov, L. S. Minushkina, “Monotonicity of the Poincaré mapping in some models of circular gene networks”, Sib. Zh. Ind. Mat., 22:3 (2019), 39–47; J. Appl. Industr. Math., 13:3 (2019), 472–479
Citation in format AMSBIB
\Bibitem{GolMin19}
\by V.~P.~Golubyatnikov, L.~S.~Minushkina
\paper Monotonicity of the Poincar\'{e} mapping in some models of circular gene networks
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 3
\pages 39--47
\mathnet{http://mi.mathnet.ru/sjim1052}
\crossref{https://doi.org/10.33048/sibjim.2019.22.304
}
\elib{https://elibrary.ru/item.asp?id=41633441}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 3
\pages 472--479
\crossref{https://doi.org/10.1134/S1990478919030086}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071434868}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
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