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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 4, Pages 19–25
DOI: https://doi.org/10.33048/sibjim.2019.22.402 (Mi sjim1061) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Structure of the phase portrait of a piecewise-linear dynamical system

N. B. Ayupovaab, V. P. Golubyatnikovac

a Sobolev Institute of Mathematics SB RAS, pr. Akad. Koptyuga 4, 630090 Novosibirsk
b Novosibirsk State University, ul. Pirogova 1, 630090 Novosibirsk
c Yakovlev Novosibirsk Military Institute, ul. Kluch-Kamyshenskoe Plato 6/2, 630114 Novosibirsk
Full-text PDF (211 kB) Citations (4)
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DOI: https://doi.org/10.33048/sibjim.2019.22.402
Abstract: We consider some piecewise linear $4$-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass–Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.
Keywords: block-linear dynamical systems, phase portraits, invariant surfaces, cycles, Poincaré mapping, gene network models, Hopf link.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00057_a
Siberian Branch of Russian Academy of Sciences I.1.5 (проект 0314-2018-0011)
The authors were supported by the Russian Foundation for Basic Research (project no. 18-01-00057) and Program No. I.5.1 of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2018-0011).
Received: 05.07.2019
Revised: 05.07.2019
Accepted: 05.09.2019
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 4, Pages 606–611
DOI: https://doi.org/10.1134/S1990478919040033
Document Type: Article
UDC: 514.763.81
Language: Russian
Citation: N. B. Ayupova, V. P. Golubyatnikov, “Structure of the phase portrait of a piecewise-linear dynamical system”, Sib. Zh. Ind. Mat., 22:4 (2019), 19–25; J. Appl. Industr. Math., 13:4 (2019), 606–611
Citation in format AMSBIB
\Bibitem{AyuGol19}
\by N.~B.~Ayupova, V.~P.~Golubyatnikov
\paper Structure of the phase portrait of a piecewise-linear dynamical system
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 4
\pages 19--25
\mathnet{http://mi.mathnet.ru/sjim1061}
\crossref{https://doi.org/10.33048/sibjim.2019.22.402}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 4
\pages 606--611
\crossref{https://doi.org/10.1134/S1990478919040033}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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