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

Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika

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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 10 scientific papers (total in 10 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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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
V. P. Golubyatnikov, V. V. Ivanov, L. S. Minushkina, “O suschestvovanii tsikla v odnoi nesimmetrichnoi modeli koltsevoi gennoi seti”, Sib. zhurn. chist. i prikl. matem., 18:3 (2018), 27–35
V. P. Golubyatnikov, V. S. Gradov, “O needinstvennosti tsiklov v nekotorykh kusochno-lineinykh modelyakh koltsevykh gennykh setei”, Matem. tr., 23:1 (2020), 107–122
V. P. Golubyatnikov, L. S. Minushkina, “On uniqueness and stability of a cycle in one gene network”, Sib. elektron. matem. izv., 18:1 (2021), 464–473

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

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