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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2012, Volume 12, Issue 2, Pages 3–12
(Mi vngu114)
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This article is cited in 9 scientific papers (total in 9 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.
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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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http://mi.mathnet.ru/eng/vngu114 http://mi.mathnet.ru/eng/vngu/v12/i2/p3
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:
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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
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A. A. Akinshin, “Bifurkatsiya Andronova–Khopfa dlya nekotorykh nelineinykh uravnenii s zapazdyvaniem”, Sib. zhurn. industr. matem., 16:3 (2013), 3–15
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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
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M. V. Kazantsev, “O nekotorykh svoistvakh grafov domenov dinamicheskikh sistem”, Sib. zhurn. industr. matem., 18:4 (2015), 42–48
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V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483
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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
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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
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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
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V. P. Golubyatnikov, V. S. Gradov, “O needinstvennosti tsiklov v nekotorykh kusochno-lineinykh modelyakh koltsevykh gennykh setei”, Matem. tr., 23:1 (2020), 107–122
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