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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2012, Volume 12, Issue 2, Pages 3–12 (Mi vngu114)  

This article is cited in 5 scientific papers (total in 5 papers)

Geometric characteristics of cycles in some symmetric dynamical systems

A. A. Akinshina, V. P. Golubyatnikovbc

a Altai State Technical University, Barnaul, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
c Novosibirsk State University, Novosibirsk, Russia

Abstract: We show non-uniqueness of cycles in phase portraits of some odd-dimensional nonlinear dynamical systems considered as models of gene networks regulated by negative feedbacks. We find geometric and analytic characteristics of these cycles and construct a graph, which describes qualitative behavior of trajectories of these dynamical systems.

Keywords: gene networks models, nonlinear dynamical systems, stationary points, invariant domains, periodic trajectories, unstable cycles, graphs, numerical modeling.

Full text: PDF file (883 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 514.745.82
Received: 03.02.2012

Citation: A. A. Akinshin, V. P. Golubyatnikov, “Geometric characteristics of cycles in some symmetric dynamical systems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:2 (2012), 3–12

Citation in format AMSBIB
\Bibitem{AkiGol12}
\by A.~A.~Akinshin, V.~P.~Golubyatnikov
\paper Geometric characteristics of cycles in some symmetric dynamical systems
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2012
\vol 12
\issue 2
\pages 3--12
\mathnet{http://mi.mathnet.ru/vngu114}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Akinshin, V. P. Golubyatnikov, I. V. Golubyatnikov, “O nekotorykh mnogomernykh modelyakh funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matem., 16:1 (2013), 3–9  mathnet  mathscinet
    2. A. A. Akinshin, “Bifurkatsiya Andronova–Khopfa dlya nekotorykh nelineinykh uravnenii s zapazdyvaniem”, Sib. zhurn. industr. matem., 16:3 (2013), 3–15  mathnet  mathscinet
    3. N. B. Ayupova, V. P. Golubyatnikov, “On two classes of nonlinear dynamical systems: The four-dimensional case”, Siberian Math. J., 56:2 (2015), 231–236  mathnet  crossref  mathscinet  isi  elib  elib
    4. M. V. Kazantsev, “O nekotorykh svoistvakh grafov domenov dinamicheskikh sistem”, Sib. zhurn. industr. matem., 18:4 (2015), 42–48  mathnet  crossref  mathscinet  elib
    5. 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
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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