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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 2, Pages 121–129
DOI: https://doi.org/10.15372/SJNM20170201 (Mi sjvm640) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On existence of a cycle in one asymmetric model of a molecular repressilator

N. B. Ayupovaab, V. P. Golubyatnikovab, M. V. Kazantsevc

a Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, 630090, Russia
b Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
c Polzunov Altai State Technical University, Lenina avenue, 46, Barnaul, Altai region, 656038, Russia
Full-text PDF (665 kB) Citations (11)
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DOI: https://doi.org/10.15372/SJNM20170201
Abstract: We consider a nonlinear 6-dimensional dynamic system which is a model of functioning of one simple molecular repressilator and find sufficient conditions of existence of a cycle C in the phase portrait of this system. An invariant neighborhood of C which retracts to C has been constructed.
Key words: nonlinear dynamical systems, gene networks models, phase portrait's discretization, hyperbolic equilibrium points, cycles, Brower's fixed point theorem.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00745
Received: 22.09.2016
Revised: 26.12.2016
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 2, Pages 101–107
DOI: https://doi.org/10.1134/S199542391702001X
Bibliographic databases:
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: N. B. Ayupova, V. P. Golubyatnikov, M. V. Kazantsev, “On existence of a cycle in one asymmetric model of a molecular repressilator”, Sib. Zh. Vychisl. Mat., 20:2 (2017), 121–129; Num. Anal. Appl., 10:2 (2017), 101–107
Citation in format AMSBIB
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\paper On existence of a~cycle in one asymmetric model of a~molecular repressilator
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  • https://www.mathnet.ru/eng/sjvm640
  • https://www.mathnet.ru/eng/sjvm/v20/i2/p121
    • This publication is cited in the following 11 articles:
    1. V. P. Golubyatnikov, “O needinstvennosti tsiklov v trekhmernykh modelyakh koltsevykh gennykh setei”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 23–34  mathnet  crossref
    2. V. P. Golubyatnikov, N. E. Kirillova, L. S. Minushkina, “Chislennoe i matematicheskoe modelirovanie gennoi seti s nelineinoi degradatsiei komponent”, Sib. zhurn. vychisl. matem., 27:1 (2024), 1–10  mathnet  crossref
    3. 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  crossref
    4. Vladimir Golubyatnikov, Natalia Ayupova, Natalia Kirillova, “On Oscillations in a Gene Network with Diffusion”, Mathematics, 11:8 (2023), 1951  crossref
    5. 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  mathnet  crossref  crossref  mathscinet
    6. A. A. Akinshin, N. B. Ayupova, V. P. Golubyatnikov, N. E. Kirillova, O. A. Podkolodnaya, N. L. Podkolodnyi, “Ob odnoi chislennoi modeli tsirkadnogo ostsillyatora”, Sib. zhurn. vychisl. matem., 25:3 (2022), 227–240  mathnet  crossref
    7. A. A Akinshin, N. B Ayupova, V. P Golubyatnikov, N. E Kirillova, O. A Podkolodnaya, N. L Podkolodnyy, “On a Numerical Model of a Circadian Oscillator”, Numer. Analys. Appl., 15:3 (2022), 187  crossref
    8. N. E. Kirillova, “On invariant surfaces in gene network models”, J. Appl. Industr. Math., 14:4 (2020), 666–671  mathnet  crossref  crossref  elib
    9. 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  mathnet  crossref  crossref  elib
    10. V. P. Golubyatnikov, T. A. Bukharina, M. V. Kazantsev, N. E. Kirillova, “Mathematical and numerical models of two asymmetric gene networks”, Sib. Electron. Math. Rep., 15 (2018), 1271–1283  mathnet  crossref  mathscinet  zmath  isi
    11. V. P. Golubyatnikov, N. E. Kirillova, “On cycles in models of functioning of circular gene networks”, J. Math. Sci., 246:6 (2020), 779–787  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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