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

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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 7 scientific papers (total in 7 papers)

Geometric characteristics of cycles in some symmetric dynamical systems

A. A. Akinshin^a, V. P. Golubyatnikov^bc

^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.

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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:

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
A. A. Akinshin, “Bifurkatsiya Andronova–Khopfa dlya nekotorykh nelineinykh uravnenii s zapazdyvaniem”, Sib. zhurn. industr. matem., 16:3 (2013), 3–15
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
M. V. Kazantsev, “O nekotorykh svoistvakh grafov domenov dinamicheskikh sistem”, Sib. zhurn. industr. matem., 18:4 (2015), 42–48
V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483
V. P. Golubyatnikov, M. V. Kazantsev, “On one piecewise linear dynamical system which models a gene network with variable feedback”, J. Math. Sci., 230:1 (2018), 46–54
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

Вестник Новосибирского государственного университета. Серия: математика, механика, информатика

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