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 $\mathcal C$ in the phase portrait of this system. An invariant neighborhood of $\mathcal C$ which retracts to $\mathcal C$ 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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\pages 121--129
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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