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Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System. / Glubokikh, A. V.

In: Siberian Advances in Mathematics, Vol. 35, No. 1, 2025, p. 1-6.

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

Harvard

Glubokikh, AV 2025, 'Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System', Siberian Advances in Mathematics, vol. 35, no. 1, pp. 1-6. https://doi.org/10.1134/S1055134425010018

APA

Glubokikh, A. V. (2025). Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System. Siberian Advances in Mathematics, 35(1), 1-6. https://doi.org/10.1134/S1055134425010018

Vancouver

Glubokikh AV. Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System. Siberian Advances in Mathematics. 2025;35(1):1-6. doi: 10.1134/S1055134425010018

Author

Glubokikh, A. V. / Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System. In: Siberian Advances in Mathematics. 2025 ; Vol. 35, No. 1. pp. 1-6.

BibTeX

@article{041474779cd24268bbc55f7991edbd7d,
title = "Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System",
abstract = "Abstract: We study the structure of the phase portrait of a three-dimensional dynamical systemsimulating functioning of a simple molecular repressilator. We prove that there exists a uniqueasymptotically stable equilibrium point and find conditions for existence and stability of a closedtrajectory located outside the domain of attraction of this point.",
keywords = "Gene network models, dynamical systems, nonlocal oscillations, periodic solutions, phase portraits, stationary points, step functions",
author = "Glubokikh, {A. V.}",
year = "2025",
doi = "10.1134/S1055134425010018",
language = "English",
volume = "35",
pages = "1--6",
journal = "Siberian Advances in Mathematics",
issn = "1055-1344",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Stability of Nonlocal Oscillations in a Piecewise-Linear Dynamical System

AU - Glubokikh, A. V.

PY - 2025

Y1 - 2025

N2 - Abstract: We study the structure of the phase portrait of a three-dimensional dynamical systemsimulating functioning of a simple molecular repressilator. We prove that there exists a uniqueasymptotically stable equilibrium point and find conditions for existence and stability of a closedtrajectory located outside the domain of attraction of this point.

AB - Abstract: We study the structure of the phase portrait of a three-dimensional dynamical systemsimulating functioning of a simple molecular repressilator. We prove that there exists a uniqueasymptotically stable equilibrium point and find conditions for existence and stability of a closedtrajectory located outside the domain of attraction of this point.

KW - Gene network models

KW - dynamical systems

KW - nonlocal oscillations

KW - periodic solutions

KW - phase portraits

KW - stationary points

KW - step functions

UR - https://www.mendeley.com/catalogue/5beb3137-eb18-34d0-b71d-b2d14d09ca0c/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105010078693&origin=inward

U2 - 10.1134/S1055134425010018

DO - 10.1134/S1055134425010018

M3 - Article

VL - 35

SP - 1

EP - 6

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -

ID: 68467670