Properties of solutions to one class of nonlinear systems of differential equations with a parameter

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Properties of solutions to one class of nonlinear systems of differential equations with a parameter. / Denisiuk, V. A.; Matveeva, I. I.

In: Chelyabinsk Physical and Mathematical Journal, Vol. 8, No. 4, 2023, p. 483-501.

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

BibTeX

@article{af3dda96bf3a40318828879710b8a5a1,

title = "Properties of solutions to one class of nonlinear systems of differential equations with a parameter",

abstract = "A system of nonlinear ordinary differential equations of large dimension with a parameter is considered. We investigate asymptotic properties of solutions to the system in dependence on the growth of the number of the equations or parameter. We prove that, for sufficiently large number of differential equations, the last component of the solution to the Cauchy problem is an approximate solution to an initial problem for one delay differential equation. For a fixed number of equations and a sufficiently large parameter, the solution to the Cauchy problem for the system is an approximate solution to the Cauchy problem for a simpler system.",

keywords = "asymptotic properties of solutions, delay differential equation, system of ordinary differential equations of large dimension",

author = "Denisiuk, {V. A.} and Matveeva, {I. I.}",

note = "The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008). Публикация для корректировки.",

year = "2023",

doi = "10.47475/2500-0101-2023-8-4-483-501",

language = "English",

volume = "8",

pages = "483--501",

journal = "Chelyabinsk Physical and Mathematical Journal",

issn = "2500-0101",

publisher = "Chelyabinsk State University",

number = "4",

}

RIS

TY - JOUR

T1 - Properties of solutions to one class of nonlinear systems of differential equations with a parameter

AU - Denisiuk, V. A.

AU - Matveeva, I. I.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008). Публикация для корректировки.

PY - 2023

Y1 - 2023

N2 - A system of nonlinear ordinary differential equations of large dimension with a parameter is considered. We investigate asymptotic properties of solutions to the system in dependence on the growth of the number of the equations or parameter. We prove that, for sufficiently large number of differential equations, the last component of the solution to the Cauchy problem is an approximate solution to an initial problem for one delay differential equation. For a fixed number of equations and a sufficiently large parameter, the solution to the Cauchy problem for the system is an approximate solution to the Cauchy problem for a simpler system.

AB - A system of nonlinear ordinary differential equations of large dimension with a parameter is considered. We investigate asymptotic properties of solutions to the system in dependence on the growth of the number of the equations or parameter. We prove that, for sufficiently large number of differential equations, the last component of the solution to the Cauchy problem is an approximate solution to an initial problem for one delay differential equation. For a fixed number of equations and a sufficiently large parameter, the solution to the Cauchy problem for the system is an approximate solution to the Cauchy problem for a simpler system.

KW - asymptotic properties of solutions

KW - delay differential equation

KW - system of ordinary differential equations of large dimension

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85178326918&origin=inward&txGid=64b9bef68a5b866a89773fb89dcdd21f

UR - https://www.mendeley.com/catalogue/09f3f236-55a3-30e2-8b4b-5bb2d1a7c64f/

U2 - 10.47475/2500-0101-2023-8-4-483-501

DO - 10.47475/2500-0101-2023-8-4-483-501

M3 - Article

VL - 8

SP - 483

EP - 501

JO - Chelyabinsk Physical and Mathematical Journal

JF - Chelyabinsk Physical and Mathematical Journal

SN - 2500-0101

IS - 4

ER -

ID: 59774089