On a Cycle in a 5-Dimensional Circular Gene Network Model

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On a Cycle in a 5-Dimensional Circular Gene Network Model. / Ayupova, N. B.; Golubyatnikov, V. P.

In: Journal of Applied and Industrial Mathematics, Vol. 15, No. 3, 2, 08.2021, p. 376-383.

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

Harvard

Ayupova, NB & Golubyatnikov, VP 2021, 'On a Cycle in a 5-Dimensional Circular Gene Network Model', Journal of Applied and Industrial Mathematics, vol. 15, no. 3, 2, pp. 376-383. https://doi.org/10.1134/S1990478921030029

APA

Ayupova, N. B., & Golubyatnikov, V. P. (2021). On a Cycle in a 5-Dimensional Circular Gene Network Model. Journal of Applied and Industrial Mathematics, 15(3), 376-383. [2]. https://doi.org/10.1134/S1990478921030029

Vancouver

Ayupova NB , Golubyatnikov VP. On a Cycle in a 5-Dimensional Circular Gene Network Model. Journal of Applied and Industrial Mathematics. 2021 Aug;15(3):376-383. 2. doi: 10.1134/S1990478921030029

Author

Ayupova, N. B. ; Golubyatnikov, V. P. / On a Cycle in a 5-Dimensional Circular Gene Network Model. In: Journal of Applied and Industrial Mathematics. 2021 ; Vol. 15, No. 3. pp. 376-383.

BibTeX

@article{9bbc40bb92a3494db6d4425de5a7da43,

title = "On a Cycle in a 5-Dimensional Circular Gene Network Model",

abstract = "The necessary and sufficient conditions are obtained for the uniqueness of a cycle in thephase portrait of a piecewise linear dynamical system that simulates functioning a gene networkwith five components regulated by negative feedbacks only. We describe the behavior oftrajectories of this system in the invariant domain homeomorphic to a torus and prove thestability of this cycle.",

keywords = "circular gene network model, cycle, fixed point, invariant domain, monotonicity, negative feedback, phase portrait, piecewise-linear dynamical system, Poincar{\'e} map, stability",

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

note = "Funding Information: The authors were supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0011). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = aug,

doi = "10.1134/S1990478921030029",

language = "English",

volume = "15",

pages = "376--383",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - On a Cycle in a 5-Dimensional Circular Gene Network Model

AU - Ayupova, N. B.

AU - Golubyatnikov, V. P.

PY - 2021/8

Y1 - 2021/8

N2 - The necessary and sufficient conditions are obtained for the uniqueness of a cycle in thephase portrait of a piecewise linear dynamical system that simulates functioning a gene networkwith five components regulated by negative feedbacks only. We describe the behavior oftrajectories of this system in the invariant domain homeomorphic to a torus and prove thestability of this cycle.

AB - The necessary and sufficient conditions are obtained for the uniqueness of a cycle in thephase portrait of a piecewise linear dynamical system that simulates functioning a gene networkwith five components regulated by negative feedbacks only. We describe the behavior oftrajectories of this system in the invariant domain homeomorphic to a torus and prove thestability of this cycle.

KW - circular gene network model

KW - cycle

KW - fixed point

KW - invariant domain

KW - monotonicity

KW - negative feedback

KW - phase portrait

KW - piecewise-linear dynamical system

KW - Poincaré map

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85126385087&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/b18bc015-5726-3d10-8c36-e275b639dbde/

U2 - 10.1134/S1990478921030029

DO - 10.1134/S1990478921030029

M3 - Article

AN - SCOPUS:85126385087

VL - 15

SP - 376

EP - 383

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

M1 - 2

ER -

ID: 35703696