A. A. Akinshin, V. P. Golubyatnikov, I. V. Golubyatnikov, “On some many-dimensional models of the functioning of gene networks”, Sib. Zh. Ind. Mat., 16:1 (2013), 3–9; J. Appl. Industr. Math., 7:3 (2013), 296

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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 1, Pages 3–9 (Mi sjim761)

This article is cited in 11 scientific papers (total in 11 papers)

On some many-dimensional models of the functioning of gene networks

A. A. Akinshin^a, V. P. Golubyatnikov^b, I. V. Golubyatnikov^b

^a Polzunov Altay State Technical University, Barnaul, Russia
^b Sobolev Institute of Mathematics of the SDRAS, Novosibirsk, Russia

Full-text PDF (211 kB) Citations (11)

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Abstract: We obtain a sufficient condition for the nonuniqueness of cycles in some nonlinear dynamical systems considered as models of the functioning of gene networks. Some constructive methods of determination of these cycles and invariant surfaces containing these cycles are described as well.

Keywords: nonlinear dynamical systems, gene networks models, phase portraits, invariant domains, stationary points, cycles.

Received: 21.01.2013

English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 3, Pages 296–301
DOI: https://doi.org/10.1134/S1990478913030022

Bibliographic databases:

Document Type: Article

UDC: 514.745.82

Language: Russian

Citation: A. A. Akinshin, V. P. Golubyatnikov, I. V. Golubyatnikov, “On some many-dimensional models of the functioning of gene networks”, Sib. Zh. Ind. Mat., 16:1 (2013), 3–9; J. Appl. Industr. Math., 7:3 (2013), 296–301

Citation in format AMSBIB

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\pages 3--9

\mathnet{http://mi.mathnet.ru/sjim761}

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\jour J. Appl. Industr. Math.

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\crossref{https://doi.org/10.1134/S1990478913030022}

Linking options:

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https://www.mathnet.ru/eng/sjim/v16/i1/p3

This publication is cited in the following 11 articles:

Vladimir P. Golubyatnikov, Natalia B. Ayupova, Natalia E. Bondarenko, Alina V. Glubokikh, “Hidden attractors and nonlocal oscillations in gene networks models”, Russian Journal of Numerical Analysis and Mathematical Modelling, 39:2 (2024), 75
V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina, “Stratifications and foliations in phase portraits of gene network models”, Vestn. VOGiS, 26:8 (2023), 758
N. B. Ayupova, V. P. Golubyatnikov, “Ob odnom tsikle v pyatimernoi modeli koltsevoi gennoi seti”, Sib. zhurn. industr. matem., 24:3 (2021), 19–29
N. B. Ayupova, V. P. Golubyatnikov, “On a Cycle in a $5$-Dimensional Circular Gene Network Model”, J. Appl. Ind. Math., 15:3 (2021), 376
Likhoshvai V.A., Golubyatnikov V.P., Khlebodarova T.M., “Limit Cycles in Models of Circular Gene Networks Regulated By Negative Feedback Loops”, BMC Bioinformatics, 21:11, SI (2020), 255
N. B. Ayupova, V. P. Golubyatnikov, “Structure of the phase portrait of a piecewise-linear dynamical system”, J. Appl. Industr. Math., 13:4 (2019), 606–611
V. P. Golubyatnikov, V. V. Ivanov, “Cycles in the odd-dimensional models of circular gene networks”, J. Appl. Industr. Math., 12:4 (2018), 648–657
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
V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483
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
A. A. Akinshin, “Bifurkatsiya Andronova–Khopfa dlya nekotorykh nelineinykh uravnenii s zapazdyvaniem”, Sib. zhurn. industr. matem., 16:3 (2013), 3–15

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

Сибирский журнал индустриальной математики

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