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Stability of autoresonance models. / Kalyakin, L. A.; Sultanov, O. A.

в: Differential Equations, Том 49, № 3, 01.03.2013, стр. 267-281.

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

Harvard

Kalyakin, LA & Sultanov, OA 2013, 'Stability of autoresonance models', Differential Equations, Том. 49, № 3, стр. 267-281. https://doi.org/10.1134/S0012266113030014

APA

Kalyakin, L. A., & Sultanov, O. A. (2013). Stability of autoresonance models. Differential Equations, 49(3), 267-281. https://doi.org/10.1134/S0012266113030014

Vancouver

Kalyakin LA, Sultanov OA. Stability of autoresonance models. Differential Equations. 2013 Март 1;49(3):267-281. https://doi.org/10.1134/S0012266113030014

Author

Kalyakin, L. A. ; Sultanov, O. A. / Stability of autoresonance models. в: Differential Equations. 2013 ; Том 49, № 3. стр. 267-281.

BibTeX

@article{c8b9e8cdf3f74566a2862518f9eaa2ec,
title = "Stability of autoresonance models",
abstract = "We consider systems of two nonlinear nonautonomous differential equations on the real line which arise when averaging rapid nonlinear vibrations. We study the Lyapunov stability of solutions with infinitely increasing amplitude. Such solutions are related to the description of the initial stage of autoresonance or resonance trapping in oscillating nonlinear systems with a small perturbation. We obtain conditions on the coefficients of the equations under which the increasing solutions are stable or unstable. The problem is reduced to the analysis of an equilibrium. The stability of the equilibrium is studied by the Lyapunov second method. The construction of Lyapunov functions is based the presence of dissipative terms with coefficients moderately decaying in time. {\textcopyright} 2013 Pleiades Publishing, Ltd.",
author = "Kalyakin, {L. A.} and Sultanov, {O. A.}",
year = "2013",
month = mar,
day = "1",
doi = "10.1134/S0012266113030014",
language = "English",
volume = "49",
pages = "267--281",
journal = "Differential Equations",
issn = "0012-2661",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Stability of autoresonance models

AU - Kalyakin, L. A.

AU - Sultanov, O. A.

PY - 2013/3/1

Y1 - 2013/3/1

N2 - We consider systems of two nonlinear nonautonomous differential equations on the real line which arise when averaging rapid nonlinear vibrations. We study the Lyapunov stability of solutions with infinitely increasing amplitude. Such solutions are related to the description of the initial stage of autoresonance or resonance trapping in oscillating nonlinear systems with a small perturbation. We obtain conditions on the coefficients of the equations under which the increasing solutions are stable or unstable. The problem is reduced to the analysis of an equilibrium. The stability of the equilibrium is studied by the Lyapunov second method. The construction of Lyapunov functions is based the presence of dissipative terms with coefficients moderately decaying in time. © 2013 Pleiades Publishing, Ltd.

AB - We consider systems of two nonlinear nonautonomous differential equations on the real line which arise when averaging rapid nonlinear vibrations. We study the Lyapunov stability of solutions with infinitely increasing amplitude. Such solutions are related to the description of the initial stage of autoresonance or resonance trapping in oscillating nonlinear systems with a small perturbation. We obtain conditions on the coefficients of the equations under which the increasing solutions are stable or unstable. The problem is reduced to the analysis of an equilibrium. The stability of the equilibrium is studied by the Lyapunov second method. The construction of Lyapunov functions is based the presence of dissipative terms with coefficients moderately decaying in time. © 2013 Pleiades Publishing, Ltd.

UR - http://www.scopus.com/inward/record.url?scp=84878204744&partnerID=8YFLogxK

U2 - 10.1134/S0012266113030014

DO - 10.1134/S0012266113030014

M3 - Article

AN - SCOPUS:84878204744

VL - 49

SP - 267

EP - 281

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 3

ER -

ID: 126273631