Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations

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Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations. / Султанов, Оскар Анварович.

In: Communications on Pure and Applied Analysis, Vol. 23, No. 4, 01.04.2024, p. 432–462.

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

BibTeX

@article{13d092008edc4cc7b98abe33eb5a99c5,

title = "Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations",

abstract = "A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic perturbations of white noise type on the stability of the system is discussed. It is shown that different long-term asymptotic regimes for solutions are admissible in the system and the stochastic stability of the equilibrium depends on the realized regime. In particular, we show that stable phase locking is possible in the system due to decaying stochastic perturbations. The proposed analysis is based on a combination of the averaging technique and the construction of stochastic Lyapunov functions.",

keywords = "Asymptotically autonomous system, phase drifting, phase locking, stability, stochastic Lyapunov function, stochastic perturbation",

author = "Султанов, {Оскар Анварович}",

year = "2024",

month = apr,

day = "1",

doi = "10.3934/cpaa.2024018",

language = "English",

volume = "23",

pages = "432–462",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}

RIS

TY - JOUR

T1 - Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations

AU - Султанов, Оскар Анварович

PY - 2024/4/1

Y1 - 2024/4/1

N2 - A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic perturbations of white noise type on the stability of the system is discussed. It is shown that different long-term asymptotic regimes for solutions are admissible in the system and the stochastic stability of the equilibrium depends on the realized regime. In particular, we show that stable phase locking is possible in the system due to decaying stochastic perturbations. The proposed analysis is based on a combination of the averaging technique and the construction of stochastic Lyapunov functions.

AB - A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic perturbations of white noise type on the stability of the system is discussed. It is shown that different long-term asymptotic regimes for solutions are admissible in the system and the stochastic stability of the equilibrium depends on the realized regime. In particular, we show that stable phase locking is possible in the system due to decaying stochastic perturbations. The proposed analysis is based on a combination of the averaging technique and the construction of stochastic Lyapunov functions.

KW - Asymptotically autonomous system

KW - phase drifting

KW - phase locking

KW - stability

KW - stochastic Lyapunov function

KW - stochastic perturbation

UR - https://www.mendeley.com/catalogue/27a05965-43ca-31db-bd52-9f6128e19c19/

U2 - 10.3934/cpaa.2024018

DO - 10.3934/cpaa.2024018

M3 - Article

VL - 23

SP - 432

EP - 462

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

SN - 1534-0392

IS - 4

ER -

ID: 126276040