Nonlinear resonance in oscillatory systems with decaying perturbations

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Nonlinear resonance in oscillatory systems with decaying perturbations. / Султанов, Оскар Анварович.

In: Discrete and Continuous Dynamical Systems, Vol. 45, No. 5, 01.05.2025, p. 1691–1719.

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

BibTeX

@article{4a22b99e395548bfad3d5fddf03b42ed,

title = "Nonlinear resonance in oscillatory systems with decaying perturbations",

abstract = "Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance effects and long-term asymptotic regimes for solutions are investigated. In particular, the emergence of stable states close to periodic ones is discussed. By combining the averaging technique, stability analysis, and constructing suitable Lyapunov functions, the conditions on perturbations are described that guarantee the existence and stability of the phase-locking regime with a resonant amplitude. The results obtained are applied to the perturbed Duffing oscillator.",

keywords = "Nonlinear oscillator, asymptotic behaviour, averaging, decaying perturbation, nonlinear resonance, phase locking, stability",

author = "Султанов, {Оскар Анварович}",

year = "2025",

month = may,

day = "1",

doi = "10.3934/dcds.2024143",

language = "English",

volume = "45",

pages = "1691–1719",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "5",

}

RIS

TY - JOUR

T1 - Nonlinear resonance in oscillatory systems with decaying perturbations

AU - Султанов, Оскар Анварович

PY - 2025/5/1

Y1 - 2025/5/1

N2 - Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance effects and long-term asymptotic regimes for solutions are investigated. In particular, the emergence of stable states close to periodic ones is discussed. By combining the averaging technique, stability analysis, and constructing suitable Lyapunov functions, the conditions on perturbations are described that guarantee the existence and stability of the phase-locking regime with a resonant amplitude. The results obtained are applied to the perturbed Duffing oscillator.

AB - Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance effects and long-term asymptotic regimes for solutions are investigated. In particular, the emergence of stable states close to periodic ones is discussed. By combining the averaging technique, stability analysis, and constructing suitable Lyapunov functions, the conditions on perturbations are described that guarantee the existence and stability of the phase-locking regime with a resonant amplitude. The results obtained are applied to the perturbed Duffing oscillator.

KW - Nonlinear oscillator

KW - asymptotic behaviour

KW - averaging

KW - decaying perturbation

KW - nonlinear resonance

KW - phase locking

KW - stability

UR - https://www.mendeley.com/catalogue/0525162a-5010-336b-becb-9e9976a11dc8/

U2 - 10.3934/dcds.2024143

DO - 10.3934/dcds.2024143

M3 - Article

VL - 45

SP - 1691

EP - 1719

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 5

ER -

ID: 132620641