V. P. Golubyatnikov, I. V. Golubyatnikov, V. A. Likhoshvai, “On the existence and stability of cycles in five-dimensional models of gene networks”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 403–411; Num. Anal. Appl., 3:4 (2010), 329

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2010, Volume 13, Number 4, Pages 403–411 (Mi sjvm415)

This article is cited in 18 scientific papers (total in 18 papers)

On the existence and stability of cycles in five-dimensional models of gene networks

V. P. Golubyatnikov^ab, I. V. Golubyatnikov^a, V. A. Likhoshvai^bc

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk
^c Institute of cytology and genetics Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Full-text PDF (223 kB) Citations (18)

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Abstract: We obtain sufficient conditions for the existence and stability of closed trajectories in five-dimensional nonlinear dynamical systems which model gene networks with negative feedbacks.

Key words: gene networks, nonlinear dynamical systems, stationary points, periodic trajectories.

Received: 16.11.2009
Revised: 15.02.2010

English version:
Numerical Analysis and Applications, 2010, Volume 3, Issue 4, Pages 329–335
DOI: https://doi.org/10.1134/S199542391004004X

Bibliographic databases:

Document Type: Article

UDC: 514.745.82

Language: Russian

Citation: V. P. Golubyatnikov, I. V. Golubyatnikov, V. A. Likhoshvai, “On the existence and stability of cycles in five-dimensional models of gene networks”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 403–411; Num. Anal. Appl., 3:4 (2010), 329–335

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjvm415

https://www.mathnet.ru/eng/sjvm/v13/i4/p403

This publication is cited in the following 18 articles:

Javier del Pino, Jan Košata, Oded Zilberberg, “Limit cycles as stationary states of an extended harmonic balance ansatz”, Phys. Rev. Research, 6:3 (2024)
N. B. Ayupova, V. P. Golubyatnikov, “Ob odnom tsikle v pyatimernoi modeli koltsevoi gennoi seti”, Sib. zhurn. industr. matem., 24:3 (2021), 19–29
Lakhova T.N., Kazantsev V F., Lashin S.A., Matushkin Yu.G., “The Finding and Researching Algorithm For Potentially Oscillating Enzymatic Systems”, Vavilovskii Zhurnal Genet. Sel., 25:3 (2021), 318–330
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
V. P. Golubyatnikov, V. S. Gradov, “Non-Uniqueness of Cycles in Piecewise-Linear Models of Circular Gene Networks”, Sib. Adv. Math., 31:1 (2021), 1
V. P. Golubyatnikov, V. S. Gradov, “O needinstvennosti tsiklov v nekotorykh kusochno-lineinykh modelyakh koltsevykh gennykh setei”, Matem. tr., 23:1 (2020), 107–122
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
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, “A three-cell model of the initial stage of the development of one proneural cluster”, J. Appl. Industr. Math., 11:2 (2017), 168–173
N. B. Ayupova, V. P. Golubyatnikov, M. V. Kazantsev, “On existence of a cycle in one asymmetric model of a molecular repressilator”, Num. Anal. Appl., 10:2 (2017), 101–107
Golubyatnikov V.P., Bukharina T.A., Furman D.P., “a Model Study of the Morphogenesis of D-Melanogaster Mechanoreceptors: the Central Regulatory Circuit”, J. Bioinform. Comput. Biol., 13:1, SI (2015), 1540006
A. Yu. Gaidov, P. V. Golubyatnikov, Springer Proceedings in Mathematics & Statistics, 72, Geometry and its Applications, 2014, 225
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
S. I. Fadeev, V. V. Kogai, V. V. Mironova, N. A. Omelyanchuk, V. A. Likhoshvai, “Mathematical modeling of matter distribution in cells assembling into a ring”, Num. Anal. Appl., 6:2 (2013), 151–162
Bukharina T.A., Golubyatnikov V.P., Golubyatnikov I.V., Furman D.P., “Model investigation of central regulatory contour of gene net of D. melanogaster macrochaete morphogenesis”, Russian Journal of Developmental Biology, 43:1 (2012), 49–53
A. A. Akinshin, V. P. Golubyatnikov, “Tsikly v simmetrichnykh dinamicheskikh sistemakh”, Vestn. NGU. Ser. matem., mekh., inform., 12:2 (2012), 3–12
T. A. Bukharina, V. P. Golubyatnikov, I. V. Golubyatnikov, D. P. Furman, “Mathematical modeling of the first phase of morphogenesis of mechanoreceptors in D. melanogaster”, J. Appl. Industr. Math., 6:2 (2012), 145–149
Golubyatnikov V.P., Golubyatnikov I.V., “On periodic trajectories in odd-dimensional gene network models”, Russian J. Numer. Anal. Math. Modelling, 26:4 (2011), 397–412

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Sibirskii Zhurnal Vychislitel'noi Matematiki

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