Asymptotic Stability of Solutions to Nonlinear Difference Equations with Variable Delay and Periodic Coefficients in the Linear Terms

Standard

Asymptotic Stability of Solutions to Nonlinear Difference Equations with Variable Delay and Periodic Coefficients in the Linear Terms. / Matveeva, I. I.; Khmil’, A. V.

в: Siberian Mathematical Journal, Том 67, № 3, 25.06.2026, стр. 580-589.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{e6d013400caf4ba69e30e1dbd558be40,

title = "Asymptotic Stability of Solutions to Nonlinear Difference Equations with Variable Delay and Periodic Coefficients in the Linear Terms",

abstract = "We consider a class of systems of nonlinear differenceequations with variable delay and periodic coefficients in the linear terms.We study the asymptotic stability of the zero solution, obtain an estimate for the domain of attraction of the zero solution, and establish estimates characterizing the stabilization rates of solutions to the systems at infinity. To obtain the results, we use a Lyapunov–Krasovskii functional of a special form.",

keywords = "Lyapunov–Krasovskii functional, difference equations with delay, estimates of solutions, periodic coefficients, stabilization rate, разностные уравнения с запаздыванием, ериодические коэффициенты, функционал Ляпунова — Красовского, оценки решений, скорость стабилизации",

author = "Matveeva, {I. I.} and Khmil{\textquoteright}, {A. V.}",

note = "Matveeva, I. I. Asymptotic Stability of Solutions to Nonlinear Difference Equations with Variable Delay and Periodic Coefficients in the Linear Terms / I. I. Matveeva, A. V. Khmil' // Siberian Mathematical Journal. – 2026. – Vol. 67, No. 3. – P. 580-589. – DOI 10.1134/S0037446626030067. – EDN AKHYXS. The work was supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2025–349 with the Ministry of Science and Higher Education of the Russian Federation.",

year = "2026",

month = jun,

day = "25",

doi = "10.1134/S0037446626030067",

language = "English",

volume = "67",

pages = "580--589",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Asymptotic Stability of Solutions to Nonlinear Difference Equations with Variable Delay and Periodic Coefficients in the Linear Terms

AU - Matveeva, I. I.

AU - Khmil’, A. V.

N1 - Matveeva, I. I. Asymptotic Stability of Solutions to Nonlinear Difference Equations with Variable Delay and Periodic Coefficients in the Linear Terms / I. I. Matveeva, A. V. Khmil' // Siberian Mathematical Journal. – 2026. – Vol. 67, No. 3. – P. 580-589. – DOI 10.1134/S0037446626030067. – EDN AKHYXS. The work was supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2025–349 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2026/6/25

Y1 - 2026/6/25

N2 - We consider a class of systems of nonlinear differenceequations with variable delay and periodic coefficients in the linear terms.We study the asymptotic stability of the zero solution, obtain an estimate for the domain of attraction of the zero solution, and establish estimates characterizing the stabilization rates of solutions to the systems at infinity. To obtain the results, we use a Lyapunov–Krasovskii functional of a special form.

AB - We consider a class of systems of nonlinear differenceequations with variable delay and periodic coefficients in the linear terms.We study the asymptotic stability of the zero solution, obtain an estimate for the domain of attraction of the zero solution, and establish estimates characterizing the stabilization rates of solutions to the systems at infinity. To obtain the results, we use a Lyapunov–Krasovskii functional of a special form.

KW - Lyapunov–Krasovskii functional

KW - difference equations with delay

KW - estimates of solutions

KW - periodic coefficients

KW - stabilization rate

KW - разностные уравнения с запаздыванием

KW - ериодические коэффициенты

KW - функционал Ляпунова — Красовского

KW - оценки решений

KW - скорость стабилизации

UR - https://www.mendeley.com/catalogue/35f4e392-81c6-3d68-9756-99176885b687/

UR - https://www.scopus.com/pages/publications/105042777180

UR - https://elibrary.ru/item.asp?id=91538049

U2 - 10.1134/S0037446626030067

DO - 10.1134/S0037446626030067

M3 - Article

VL - 67

SP - 580

EP - 589

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 84797675