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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 4, Pages 3–10 (Mi vngu350)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of D. Melanogaster

A. A. Akinshina, T. A. Bukharinab, V. P. Golubyatnikovcd, D. P. Furmandb

a Altai State Technical University
b Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d Novosibirsk State University

Abstract: We consider the phase portrait of a 6-dimensional nonlinear dynamical system considered as a model of an early stage of morphogenesis of D. melanogaster, i.e., appearance of its parental cell in the proneural cluster. Sufficient conditions of existence of two stable equilibrium points of this system are described, and biological interpretation is given.

Keywords: cell complex, nonlinear dynamical systems, negative and positive feedbacks, equilibrium points, the Notch signaling pathway.

Full text: PDF file (498 kB)
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UDC: 573.2:57.017.64
Received: 12.12.2013

Citation: A. A. Akinshin, T. A. Bukharina, V. P. Golubyatnikov, D. P. Furman, “Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of D. Melanogaster”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:4 (2014), 3–10

Citation in format AMSBIB
\Bibitem{AkiBukGol14}
\by A.~A.~Akinshin, T.~A.~Bukharina, V.~P.~Golubyatnikov, D.~P.~Furman
\paper Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of~\emph{D.~Melanogaster}
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 4
\pages 3--10
\mathnet{http://mi.mathnet.ru/vngu350}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Golubyatnikov, A. E. Kalënykh, “O stroenii fazovykh portretov nekotorykh nelineinykh dinamicheskikh sistem”, Vestn. NGU. Ser. matem., mekh., inform., 15:1 (2015), 45–53  mathnet; V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483  crossref
    2. N. B. Ayupova, V. P. Golubyatnikov, “Trekhkletochnaya model rannei stadii razvitiya odnogo proneiralnogo klastera”, Sib. zhurn. industr. matem., 20:2 (2017), 15–20  mathnet  crossref  elib
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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