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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2007, Volume 7, Issue 2, Pages 19–27 (Mi vngu259)  

This article is cited in 7 scientific papers (total in 7 papers)

On some nonlinear dynamical systems modelling asymmetric gene networks

Yu. A. Gaydov, V. P. Golubyatnikov

Novosibirsk State University

Abstract: We consider a wide class of 3-dimensional nonlinear dynamical systems as models of asymmetric gene networks functioning. The networks are being considered with negative feedbacks and with different regulation mechanisms. For these dynamical systems, geometric and topological characteristics of their phase portraits are studied, necessary and sufficient conditions of periodic trajectories existence are obtained, also Andronov–Hopf bifurcations are described.

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UDC: 514.745.82

Citation: Yu. A. Gaydov, V. P. Golubyatnikov, “On some nonlinear dynamical systems modelling asymmetric gene networks”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 7:2 (2007), 19–27

Citation in format AMSBIB
\Bibitem{GaiGol07}
\by Yu.~A.~Gaydov, V.~P.~Golubyatnikov
\paper On some nonlinear dynamical systems modelling asymmetric gene networks
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2007
\vol 7
\issue 2
\pages 19--27
\mathnet{http://mi.mathnet.ru/vngu259}


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    This publication is cited in the following articles:
    1. V. P. Golubyatnikov, Yu. A. Gaidov, V. A. Likhoshvai, “O nekotorykh nelineinykh dinamicheskikh sistemakh, modeliruyuschikh nesimmetrichnye gennye seti. 2”, Vestn. NGU. Ser. matem., mekh., inform., 10:1 (2010), 18–28  mathnet
    2. V. P. Golubyatnikov, I. V. Golubyatnikov, “O periodicheskikh traektoriyakh nelineinykh dinamicheskikh sistem spetsialnogo vida”, Vestn. NGU. Ser. matem., mekh., inform., 10:3 (2010), 3–16  mathnet
    3. A. A. Akinshin, V. P. Golubyatnikov, “Tsikly v simmetrichnykh dinamicheskikh sistemakh”, Vestn. NGU. Ser. matem., mekh., inform., 12:2 (2012), 3–12  mathnet
    4. N. B. Ayupova, V. P. Golubyatnikov, “On the uniqueness of a cycle in an asymmetric $3$-dimensional model of a molecular repressilator”, J. Appl. Industr. Math., 8:2 (2014), 153–157  mathnet  crossref  mathscinet
    5. A. A. Akinshin, T. A. Bukharina, V. P. Golubyatnikov, D. P. Furman, “Matematicheskoe modelirovanie vzaimodeistviya dvukh kletok v proneiralnom klastere krylovogo imaginalnogo diska D. melanogaster”, Vestn. NGU. Ser. matem., mekh., inform., 14:4 (2014), 3–10  mathnet
    6. V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483  mathnet  crossref
    7. V. P. Golubyatnikov, N. E. Kirillova, “O tsiklakh v modelyakh funktsionirovaniya koltsevykh gennykh setei”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 54–63  mathnet  crossref
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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