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Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗. / Sultanov, Oskar.

In: SIAM Journal on Applied Mathematics, Vol. 78, No. 6, 01.01.2018, p. 3103-3118.

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

Harvard

Sultanov, O 2018, 'Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗', SIAM Journal on Applied Mathematics, vol. 78, no. 6, pp. 3103-3118. https://doi.org/10.1137/18M1194250

APA

Sultanov, O. (2018). Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗. SIAM Journal on Applied Mathematics, 78(6), 3103-3118. https://doi.org/10.1137/18M1194250

Vancouver

Sultanov O. Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗. SIAM Journal on Applied Mathematics. 2018 Jan 1;78(6):3103-3118. https://doi.org/10.1137/18M1194250

Author

Sultanov, Oskar. / Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗. In: SIAM Journal on Applied Mathematics. 2018 ; Vol. 78, No. 6. pp. 3103-3118.

BibTeX

@article{1225a793bdda4d7b8af84ad10b4d583c,
title = "Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗",
abstract = "A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the autoresonant capture. By applying the Lyapunov function method we investigate the conditions for the existence and stability of autoresonant modes and construct long-term asymptotics for stable solutions. In particular, we show that unstable regimes become stable when the system parameters pass through certain threshold values.",
keywords = "Asymptotics, Autoresonance, Averaging method, Lyapunov function, Nonlinear oscillations, Stability",
author = "Oskar Sultanov",
year = "2018",
month = jan,
day = "1",
doi = "10.1137/18M1194250",
language = "English",
volume = "78",
pages = "3103--3118",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics",
number = "6",

}

RIS

TY - JOUR

T1 - Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation ∗

AU - Sultanov, Oskar

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the autoresonant capture. By applying the Lyapunov function method we investigate the conditions for the existence and stability of autoresonant modes and construct long-term asymptotics for stable solutions. In particular, we show that unstable regimes become stable when the system parameters pass through certain threshold values.

AB - A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the autoresonant capture. By applying the Lyapunov function method we investigate the conditions for the existence and stability of autoresonant modes and construct long-term asymptotics for stable solutions. In particular, we show that unstable regimes become stable when the system parameters pass through certain threshold values.

KW - Asymptotics

KW - Autoresonance

KW - Averaging method

KW - Lyapunov function

KW - Nonlinear oscillations

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85060044867&partnerID=8YFLogxK

U2 - 10.1137/18M1194250

DO - 10.1137/18M1194250

M3 - Article

AN - SCOPUS:85060044867

VL - 78

SP - 3103

EP - 3118

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -

ID: 126273152