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Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations. / Sultanov, Oskar A.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 41, No. 12, 01.12.2021, p. 5943-5978.

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

Harvard

Sultanov, OA 2021, 'Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations', Discrete and Continuous Dynamical Systems- Series A, vol. 41, no. 12, pp. 5943-5978. https://doi.org/10.3934/dcds.2021102

APA

Sultanov, O. A. (2021). Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations. Discrete and Continuous Dynamical Systems- Series A, 41(12), 5943-5978. https://doi.org/10.3934/dcds.2021102

Vancouver

Sultanov OA. Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations. Discrete and Continuous Dynamical Systems- Series A. 2021 Dec 1;41(12):5943-5978. https://doi.org/10.3934/dcds.2021102

Author

Sultanov, Oskar A. / Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations. In: Discrete and Continuous Dynamical Systems- Series A. 2021 ; Vol. 41, No. 12. pp. 5943-5978.

BibTeX

@article{5b7a14c34fae492a9957e3d7c5b79e8f,
title = "Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations",
abstract = "The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The behaviour of the perturbed trajectories in the vicinity of the equilibrium is investigated. Depending on the structure of the perturbations, various asymptotic regimes at infinity in time are possible. In particular, a phase locking and a phase drifting can occur in the systems. The paper investigates the bifurcations associated with a change of Lyapunov stability of the equilibrium in both regimes. The proposed stability analysis is based on a combination of the averaging method and the construction of Lyapunov functions.",
keywords = "Asymptotically autonomous system, Averaging, Bifurcation, Lyapunov function, Perturbation, Stability",
author = "Sultanov, {Oskar A.}",
year = "2021",
month = dec,
day = "1",
doi = "10.3934/dcds.2021102",
language = "English",
volume = "41",
pages = "5943--5978",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "12",

}

RIS

TY - JOUR

T1 - Bifurcations in asymptotically autonomous hamiltonian systems under oscillatory perturbations

AU - Sultanov, Oskar A.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The behaviour of the perturbed trajectories in the vicinity of the equilibrium is investigated. Depending on the structure of the perturbations, various asymptotic regimes at infinity in time are possible. In particular, a phase locking and a phase drifting can occur in the systems. The paper investigates the bifurcations associated with a change of Lyapunov stability of the equilibrium in both regimes. The proposed stability analysis is based on a combination of the averaging method and the construction of Lyapunov functions.

AB - The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The behaviour of the perturbed trajectories in the vicinity of the equilibrium is investigated. Depending on the structure of the perturbations, various asymptotic regimes at infinity in time are possible. In particular, a phase locking and a phase drifting can occur in the systems. The paper investigates the bifurcations associated with a change of Lyapunov stability of the equilibrium in both regimes. The proposed stability analysis is based on a combination of the averaging method and the construction of Lyapunov functions.

KW - Asymptotically autonomous system

KW - Averaging

KW - Bifurcation

KW - Lyapunov function

KW - Perturbation

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85116552594&partnerID=8YFLogxK

U2 - 10.3934/dcds.2021102

DO - 10.3934/dcds.2021102

M3 - Article

AN - SCOPUS:85116552594

VL - 41

SP - 5943

EP - 5978

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 12

ER -

ID: 126272395