Numerical and Mathematical Modeling of a Gene Network with Nonlinear Degradation of the Components

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Numerical and Mathematical Modeling of a Gene Network with Nonlinear Degradation of the Components. / Golubyatnikov, V. P.; Kirillova, N. E.; Minushkina, L. S.

In: Numerical Analysis and Applications, Vol. 17, No. 1, 03.2024, p. 1-7.

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

BibTeX

@article{712c41b92a884b73b0bed1f4080137fb,

title = "Numerical and Mathematical Modeling of a Gene Network with Nonlinear Degradation of the Components",

abstract = "Abstract: For a 3-dimensional dynamical system considered as a model of a gene network with nonlinear degradation of its components, the uniqueness of an equilibrium point is proved. Using approaches of qualitative theory of ordinary differential equations, we find conditions of existence of a cycle of this system and describe an invariant domain which contains all such cycles in the phase portrait. Numerical experiments with trajectories of this system are conducted.",

keywords = "bifurcations, cycles, equilibrium points, fast and slow variables, gene networks models, invariant domains and toruses, nonlinear dynamical systems, phase portraits, software package STEP, stability",

author = "Golubyatnikov, {V. P.} and Kirillova, {N. E.} and Minushkina, {L. S.}",

note = "This work was supported by the Russian Science Foundation (project no. 23-21-00019).",

year = "2024",

month = mar,

doi = "10.1134/S1995423924010014",

language = "English",

volume = "17",

pages = "1--7",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Numerical and Mathematical Modeling of a Gene Network with Nonlinear Degradation of the Components

AU - Golubyatnikov, V. P.

AU - Kirillova, N. E.

AU - Minushkina, L. S.

N1 - This work was supported by the Russian Science Foundation (project no. 23-21-00019).

PY - 2024/3

Y1 - 2024/3

N2 - Abstract: For a 3-dimensional dynamical system considered as a model of a gene network with nonlinear degradation of its components, the uniqueness of an equilibrium point is proved. Using approaches of qualitative theory of ordinary differential equations, we find conditions of existence of a cycle of this system and describe an invariant domain which contains all such cycles in the phase portrait. Numerical experiments with trajectories of this system are conducted.

AB - Abstract: For a 3-dimensional dynamical system considered as a model of a gene network with nonlinear degradation of its components, the uniqueness of an equilibrium point is proved. Using approaches of qualitative theory of ordinary differential equations, we find conditions of existence of a cycle of this system and describe an invariant domain which contains all such cycles in the phase portrait. Numerical experiments with trajectories of this system are conducted.

KW - bifurcations

KW - cycles

KW - equilibrium points

KW - fast and slow variables

KW - gene networks models

KW - invariant domains and toruses

KW - nonlinear dynamical systems

KW - phase portraits

KW - software package STEP

KW - stability

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187790095&origin=inward&txGid=05473ec2620851b4085f70be62b56942

UR - https://www.mendeley.com/catalogue/bcf83ea5-2b47-35ee-87f8-dbaf6577fab6/

U2 - 10.1134/S1995423924010014

DO - 10.1134/S1995423924010014

M3 - Article

VL - 17

SP - 1

EP - 7

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -

ID: 61124849