Structure of the Phase Portrait of a Piecewise-Linear Dynamical System

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Structure of the Phase Portrait of a Piecewise-Linear Dynamical System. / Ayupova, N. B.; Golubyatnikov, V. P.

In: Journal of Applied and Industrial Mathematics, Vol. 13, No. 4, 01.10.2019, p. 606-611.

Research output: Contribution to journal › Article › peer-review

Harvard

Ayupova, NB & Golubyatnikov, VP 2019, 'Structure of the Phase Portrait of a Piecewise-Linear Dynamical System', Journal of Applied and Industrial Mathematics, vol. 13, no. 4, pp. 606-611. https://doi.org/10.1134/S1990478919040033

APA

Ayupova, N. B., & Golubyatnikov, V. P. (2019). Structure of the Phase Portrait of a Piecewise-Linear Dynamical System. Journal of Applied and Industrial Mathematics, 13(4), 606-611. https://doi.org/10.1134/S1990478919040033

Vancouver

Ayupova NB , Golubyatnikov VP. Structure of the Phase Portrait of a Piecewise-Linear Dynamical System. Journal of Applied and Industrial Mathematics. 2019 Oct 1;13(4):606-611. doi: 10.1134/S1990478919040033

Author

Ayupova, N. B. ; Golubyatnikov, V. P. / Structure of the Phase Portrait of a Piecewise-Linear Dynamical System. In: Journal of Applied and Industrial Mathematics. 2019 ; Vol. 13, No. 4. pp. 606-611.

BibTeX

@article{06d4dbcea857443eb4116841dc0f03b9,

title = "Structure of the Phase Portrait of a Piecewise-Linear Dynamical System",

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 system, cycle, gene network model, Hopf link, invariant surface, phase portrait, Poincar{\'e} mapping",

author = "Ayupova, {N. B.} and Golubyatnikov, {V. P.}",

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = oct,

day = "1",

doi = "10.1134/S1990478919040033",

language = "English",

volume = "13",

pages = "606--611",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - Structure of the Phase Portrait of a Piecewise-Linear Dynamical System

AU - Ayupova, N. B.

AU - Golubyatnikov, V. P.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - block-linear dynamical system

KW - cycle

KW - gene network model

KW - Hopf link

KW - invariant surface

KW - phase portrait

KW - Poincaré mapping

UR - http://www.scopus.com/inward/record.url?scp=85078901978&partnerID=8YFLogxK

U2 - 10.1134/S1990478919040033

DO - 10.1134/S1990478919040033

M3 - Article

AN - SCOPUS:85078901978

VL - 13

SP - 606

EP - 611

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -

ID: 23428105