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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2010, Volume 13, Number 4, Pages 403–411 (Mi sjvm415)  

This article is cited in 18 scientific papers (total in 18 papers)

On the existence and stability of cycles in five-dimensional models of gene networks

V. P. Golubyatnikovab, I. V. Golubyatnikova, V. A. Likhoshvaibc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
c Institute of cytology and genetics Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: We obtain sufficient conditions for the existence and stability of closed trajectories in five-dimensional nonlinear dynamical systems which model gene networks with negative feedbacks.
Key words: gene networks, nonlinear dynamical systems, stationary points, periodic trajectories.
Received: 16.11.2009
Revised: 15.02.2010
English version:
Numerical Analysis and Applications, 2010, Volume 3, Issue 4, Pages 329–335
DOI: https://doi.org/10.1134/S199542391004004X
Bibliographic databases:
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: V. P. Golubyatnikov, I. V. Golubyatnikov, V. A. Likhoshvai, “On the existence and stability of cycles in five-dimensional models of gene networks”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 403–411; Num. Anal. Appl., 3:4 (2010), 329–335
Citation in format AMSBIB
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\by V.~P.~Golubyatnikov, I.~V.~Golubyatnikov, V.~A.~Likhoshvai
\paper On the existence and stability of cycles in five-dimensional models of gene networks
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 4
\pages 403--411
\mathnet{http://mi.mathnet.ru/sjvm415}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 4
\pages 329--335
\crossref{https://doi.org/10.1134/S199542391004004X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650410556}
Linking options:
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  • https://www.mathnet.ru/eng/sjvm/v13/i4/p403
  • This publication is cited in the following 18 articles:
    1. Javier del Pino, Jan Košata, Oded Zilberberg, “Limit cycles as stationary states of an extended harmonic balance ansatz”, Phys. Rev. Research, 6:3 (2024)  crossref
    2. N. B. Ayupova, V. P. Golubyatnikov, “Ob odnom tsikle v pyatimernoi modeli koltsevoi gennoi seti”, Sib. zhurn. industr. matem., 24:3 (2021), 19–29  mathnet  crossref
    3. Lakhova T.N., Kazantsev V F., Lashin S.A., Matushkin Yu.G., “The Finding and Researching Algorithm For Potentially Oscillating Enzymatic Systems”, Vavilovskii Zhurnal Genet. Sel., 25:3 (2021), 318–330  crossref  isi  scopus
    4. N. B. Ayupova, V. P. Golubyatnikov, “On a Cycle in a 5-Dimensional Circular Gene Network Model”, J. Appl. Ind. Math., 15:3 (2021), 376  crossref
    5. V. P. Golubyatnikov, V. S. Gradov, “Non-Uniqueness of Cycles in Piecewise-Linear Models of Circular Gene Networks”, Sib. Adv. Math., 31:1 (2021), 1  crossref
    6. V. P. Golubyatnikov, V. S. Gradov, “O needinstvennosti tsiklov v nekotorykh kusochno-lineinykh modelyakh koltsevykh gennykh setei”, Matem. tr., 23:1 (2020), 107–122  mathnet  crossref
    7. Likhoshvai V.A., Golubyatnikov V.P., Khlebodarova T.M., “Limit Cycles in Models of Circular Gene Networks Regulated By Negative Feedback Loops”, BMC Bioinformatics, 21:11, SI (2020), 255  crossref  isi  scopus
    8. V. P. Golubyatnikov, V. V. Ivanov, “Cycles in the odd-dimensional models of circular gene networks”, J. Appl. Industr. Math., 12:4 (2018), 648–657  mathnet  crossref  crossref  elib  elib
    9. N. B. Ayupova, V. P. Golubyatnikov, “A three-cell model of the initial stage of the development of one proneural cluster”, J. Appl. Industr. Math., 11:2 (2017), 168–173  mathnet  crossref  crossref  elib
    10. N. B. Ayupova, V. P. Golubyatnikov, M. V. Kazantsev, “On existence of a cycle in one asymmetric model of a molecular repressilator”, Num. Anal. Appl., 10:2 (2017), 101–107  mathnet  crossref  crossref  isi  elib
    11. Golubyatnikov V.P., Bukharina T.A., Furman D.P., “a Model Study of the Morphogenesis of D-Melanogaster Mechanoreceptors: the Central Regulatory Circuit”, J. Bioinform. Comput. Biol., 13:1, SI (2015), 1540006  crossref  isi  elib  scopus
    12. A. Yu. Gaidov, P. V. Golubyatnikov, Springer Proceedings in Mathematics & Statistics, 72, Geometry and its Applications, 2014, 225  crossref
    13. A. A. Akinshin, V. P. Golubyatnikov, I. V. Golubyatnikov, “On some many-dimensional models of the functioning of gene networks”, J. Appl. Industr. Math., 7:3 (2013), 296–301  mathnet  crossref  mathscinet
    14. S. I. Fadeev, V. V. Kogai, V. V. Mironova, N. A. Omelyanchuk, V. A. Likhoshvai, “Mathematical modeling of matter distribution in cells assembling into a ring”, Num. Anal. Appl., 6:2 (2013), 151–162  mathnet  crossref  mathscinet  elib
    15. Bukharina T.A., Golubyatnikov V.P., Golubyatnikov I.V., Furman D.P., “Model investigation of central regulatory contour of gene net of D. melanogaster macrochaete morphogenesis”, Russian Journal of Developmental Biology, 43:1 (2012), 49–53  crossref  isi  elib  scopus
    16. A. A. Akinshin, V. P. Golubyatnikov, “Tsikly v simmetrichnykh dinamicheskikh sistemakh”, Vestn. NGU. Ser. matem., mekh., inform., 12:2 (2012), 3–12  mathnet
    17. T. A. Bukharina, V. P. Golubyatnikov, I. V. Golubyatnikov, D. P. Furman, “Mathematical modeling of the first phase of morphogenesis of mechanoreceptors in D. melanogaster”, J. Appl. Industr. Math., 6:2 (2012), 145–149  mathnet  crossref  mathscinet
    18. Golubyatnikov V.P., Golubyatnikov I.V., “On periodic trajectories in odd-dimensional gene network models”, Russian J. Numer. Anal. Math. Modelling, 26:4 (2011), 397–412  crossref  mathscinet  zmath  isi  elib  scopus
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    Sibirskii Zhurnal Vychislitel'noi Matematiki
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