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Stability of autoresonance in dissipative systems. / Sultanov, Oskar Anvarovich.

In: Ufa Mathematical Journal, Vol. 7, No. 1, 01.01.2015, p. 58-69.

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

Harvard

Sultanov, OA 2015, 'Stability of autoresonance in dissipative systems', Ufa Mathematical Journal, vol. 7, no. 1, pp. 58-69. https://doi.org/10.13108/2015-7-1-58

APA

Sultanov, O. A. (2015). Stability of autoresonance in dissipative systems. Ufa Mathematical Journal, 7(1), 58-69. https://doi.org/10.13108/2015-7-1-58

Vancouver

Sultanov OA. Stability of autoresonance in dissipative systems. Ufa Mathematical Journal. 2015 Jan 1;7(1):58-69. https://doi.org/10.13108/2015-7-1-58

Author

Sultanov, Oskar Anvarovich. / Stability of autoresonance in dissipative systems. In: Ufa Mathematical Journal. 2015 ; Vol. 7, No. 1. pp. 58-69.

BibTeX

@article{5956a08996184f3ab86c13839b4076e6,
title = "Stability of autoresonance in dissipative systems",
abstract = "We consider a mathematical model describing the initial stage of a capture into autoresonance in nonlinear oscillating systems with a dissipation. Solutions whose amplitude increases unboundedly in time correspond to a resonance. An asymptotic expansion for such solutions is constructed as a power series with constant coefficients. The stability of autoresonance with respect to persistent perturbations is studied by means of Lapunov's second method. We describe the classes of perturbations for which a capture into autoresonance occurs.",
keywords = "Dissipation, Nonlinear oscillations, Perturbations, Resonance, Stability",
author = "Sultanov, {Oskar Anvarovich}",
year = "2015",
month = jan,
day = "1",
doi = "10.13108/2015-7-1-58",
language = "English",
volume = "7",
pages = "58--69",
journal = "Ufa Mathematical Journal",
issn = "2304-0122",
publisher = "Institute of Mathematics with Computer Center of Russian Academy of Sciences",
number = "1",

}

RIS

TY - JOUR

T1 - Stability of autoresonance in dissipative systems

AU - Sultanov, Oskar Anvarovich

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider a mathematical model describing the initial stage of a capture into autoresonance in nonlinear oscillating systems with a dissipation. Solutions whose amplitude increases unboundedly in time correspond to a resonance. An asymptotic expansion for such solutions is constructed as a power series with constant coefficients. The stability of autoresonance with respect to persistent perturbations is studied by means of Lapunov's second method. We describe the classes of perturbations for which a capture into autoresonance occurs.

AB - We consider a mathematical model describing the initial stage of a capture into autoresonance in nonlinear oscillating systems with a dissipation. Solutions whose amplitude increases unboundedly in time correspond to a resonance. An asymptotic expansion for such solutions is constructed as a power series with constant coefficients. The stability of autoresonance with respect to persistent perturbations is studied by means of Lapunov's second method. We describe the classes of perturbations for which a capture into autoresonance occurs.

KW - Dissipation

KW - Nonlinear oscillations

KW - Perturbations

KW - Resonance

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84937040634&partnerID=8YFLogxK

U2 - 10.13108/2015-7-1-58

DO - 10.13108/2015-7-1-58

M3 - Article

AN - SCOPUS:84937040634

VL - 7

SP - 58

EP - 69

JO - Ufa Mathematical Journal

JF - Ufa Mathematical Journal

SN - 2304-0122

IS - 1

ER -

ID: 126273514