M. V. Kazantsev, “On some properties of the domain graphs of dynamical systems”, Sib. Zh. Ind. Mat., 18:4 (2015), 42

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Sibirskii Zhurnal Industrial'noi Matematiki, 2015, Volume 18, Number 4, Pages 42–48
DOI: https://doi.org/10.17377/sibjim.2015.18.405 (Mi sjim902)

This article is cited in 16 scientific papers (total in 16 papers)

On some properties of the domain graphs of dynamical systems

M. V. Kazantsev

Polzunov Altai State Technical University, 46 Lenin av., 656038 Barnaul

Full-text PDF (229 kB) Citations (16)

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DOI: https://doi.org/10.17377/sibjim.2015.18.405

Abstract: We continue examining the properties of the domain graphs defining the discrete structure in the phase portraits of the dynamical systems modelling gene networks. Some necessary and sufficient conditions are described for the existence of cycles on different potential levels of the domain graph. Also the conditions are found for these graphs to beisomorphic for different dynamical systems.

Keywords: gene network, graph, dynamical system, potential level, phase portrait.

Received: 08.04.2015

Bibliographic databases:

Document Type: Article

UDC: 514.745.82

Language: Russian

Citation: M. V. Kazantsev, “On some properties of the domain graphs of dynamical systems”, Sib. Zh. Ind. Mat., 18:4 (2015), 42–48

Citation in format AMSBIB

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https://www.mathnet.ru/eng/sjim902

https://www.mathnet.ru/eng/sjim/v18/i4/p42

This publication is cited in the following 16 articles:

V. P. Golubyatnikov, “O needinstvennosti tsiklov v trekhmernykh modelyakh koltsevykh gennykh setei”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 23–34
A. V. Glubokikh, V. P. Golubyatnikov, “On nonlocal oscillations in 3D models of circular gene networks”, J. Appl. Industr. Math., 18:2 (2024), 246–252
L. S. Minushkina, “Periodicheskie traektorii nelineinykh modelei koltsevykh gennykh setei”, Vladikavk. matem. zhurn., 25:4 (2023), 80–90
V. P. Golubyatnikov, L. S. Minushkina, “On uniqueness of a cycle in one circular gene network model”, Siberian Math. J., 63:1 (2022), 79–86
N. B. Ayupova, V. P. Golubyatnikov, “Ob odnom tsikle v pyatimernoi modeli koltsevoi gennoi seti”, Sib. zhurn. industr. matem., 24:3 (2021), 19–29
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, “Monotonicity of the Poincaré mapping in some models of circular gene networks”, J. Appl. Industr. Math., 13:3 (2019), 472–479
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, N. E. Kirillova, “On cycles in models of functioning of circular gene networks”, J. Math. Sci., 246:6 (2020), 779–787
V. P. Golubyatnikov, M. V. Kazantsev, N. E. Kirillova, T. A. Bukharina, “Mathematical and numerical models of two asymmetric gene networks”, Sib. elektron. matem. izv., 15 (2018), 1271–1283
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
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. V. Ivanov, “Edinstvennost i ustoichivost tsikla v trekhmernykh blochno-lineinykh modelyakh koltsevykh gennykh setei”, Sib. zhurn. chist. i prikl. matem., 18:4 (2018), 19–28
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
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

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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