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Sibirskii Zhurnal Industrial'noi Matematiki, 2017, Volume 20, Number 2, Pages 15–20
DOI: https://doi.org/10.17377/sibjim.2017.20.202 (Mi sjim954) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A three-cell model of the initial stage of the development of one proneural cluster

N. B. Ayupovaab, V. P. Golubyatnikovab

a Sobolev Institute of Mathematics SB RAS, Acad. Koptyuga ave., 4, 630090 Novosibirsk
b Novosibirsk State University, Pirogova str., 2, 630090 Novosibirsk
Full-text PDF (592 kB) Citations (2)
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DOI: https://doi.org/10.17377/sibjim.2017.20.202
Abstract: We construct a $9$-dimensional nonlinear dynamical system modeling the initial stage of the interaction of three adjacent cells in a proneural cluster of Drosophila melanogaster. Conditions of existence of three stable equilibrium points in the phase portrait of this system are obtained, other equilibrium points are listed, a biological interpretation is given.
Keywords: nonlinear dynamical system, gene network, negative and positive feedback, phase portrait, equilibrium point, stability.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00745
Received: 30.06.2016
English version:
Journal of Applied and Industrial Mathematics, 2017, Volume 11, Issue 2, Pages 168–173
DOI: https://doi.org/10.1134/S1990478917020028
Bibliographic databases:
Document Type: Article
UDC: 573.2+57.017.64
Language: Russian
Citation: N. B. Ayupova, V. P. Golubyatnikov, “A three-cell model of the initial stage of the development of one proneural cluster”, Sib. Zh. Ind. Mat., 20:2 (2017), 15–20; J. Appl. Industr. Math., 11:2 (2017), 168–173
Citation in format AMSBIB
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\by N.~B.~Ayupova, V.~P.~Golubyatnikov
\paper A three-cell model of the initial stage of the development of one proneural cluster
\jour Sib. Zh. Ind. Mat.
\yr 2017
\vol 20
\issue 2
\pages 15--20
\mathnet{http://mi.mathnet.ru/sjim954}
\crossref{https://doi.org/10.17377/sibjim.2017.20.202}
\elib{https://elibrary.ru/item.asp?id=29116857}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 2
\pages 168--173
\crossref{https://doi.org/10.1134/S1990478917020028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019719918}
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  • https://www.mathnet.ru/eng/sjim954
  • https://www.mathnet.ru/eng/sjim/v20/i2/p15
    • This publication is cited in the following 2 articles:
    1. D. P. Furman, T. A. Bukharina, V. P. Golubyatnikov, “The central regulatory circuit of the morphogenesis system drosophila mechanoreceptors: mutation effects”, J. Appl. Industr. Math., 17:3 (2023), 535–543  mathnet  crossref  crossref
    2. V. P. Golubyatnikov, N. E. Kirillova, “On Cycles in Models of Functioning of Circular Gene Networks”, J Math Sci, 246:6 (2020), 779  crossref
    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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