Bifurcation of the Equilibrium of an Oscillator with a Velocity-Dependent Restoring Force under Periodic Perturbations

Standard

Bifurcation of the Equilibrium of an Oscillator with a Velocity-Dependent Restoring Force under Periodic Perturbations. / Bibikov, Yu. N. ; Bukaty, V. R. .

In: Differential Equations, Vol. 55, No. 8, 01.08.2019, p. 1011-1016.

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

BibTeX

@article{663e9d52f866483eb7760d48636d65c9,

title = "Bifurcation of the Equilibrium of an Oscillator with a Velocity-Dependent Restoring Force under Periodic Perturbations",

abstract = "We study the bifurcation of an oscillator whose restoring force depends on the velocity of motion under periodic perturbations. Separation of variables is used to derive a bifurcation equation. To each positive root of this equation, there corresponds an invariant twodimensional torus (a closed trajectory in the case of a time-independent perturbation) shrinking to the equilibrium position as the small parameter tends to zero. The proofs use methods of the Krylov-Bogolyubov theory for the case of periodic perturbations or the implicit function theorem for the case of time-independent.",

keywords = "bifurcation, oscillator, velocity-dependent restoring force, periodic perturbations, bifurcation, oscillator, velocity-dependent restoring force, periodic perturbations",

author = "Bibikov, {Yu. N.} and Bukaty, {V. R.}",

note = "Yu. N. Bibikov, V. R. Bukaty. Bifurcation of the Equilibrium of an Oscillator with a Velocity-Dependent Restoring Force under Periodic Perturbations, Differetial Equations, August 2019, Vol. 55, No 8, pp.1011-1016.",

year = "2019",

month = aug,

day = "1",

doi = "10.1134/S0012266119080020",

language = "English",

volume = "55",

pages = "1011--1016",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "8",

}

RIS

TY - JOUR

T1 - Bifurcation of the Equilibrium of an Oscillator with a Velocity-Dependent Restoring Force under Periodic Perturbations

AU - Bibikov, Yu. N.

AU - Bukaty, V. R.

N1 - Yu. N. Bibikov, V. R. Bukaty. Bifurcation of the Equilibrium of an Oscillator with a Velocity-Dependent Restoring Force under Periodic Perturbations, Differetial Equations, August 2019, Vol. 55, No 8, pp.1011-1016.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We study the bifurcation of an oscillator whose restoring force depends on the velocity of motion under periodic perturbations. Separation of variables is used to derive a bifurcation equation. To each positive root of this equation, there corresponds an invariant twodimensional torus (a closed trajectory in the case of a time-independent perturbation) shrinking to the equilibrium position as the small parameter tends to zero. The proofs use methods of the Krylov-Bogolyubov theory for the case of periodic perturbations or the implicit function theorem for the case of time-independent.

AB - We study the bifurcation of an oscillator whose restoring force depends on the velocity of motion under periodic perturbations. Separation of variables is used to derive a bifurcation equation. To each positive root of this equation, there corresponds an invariant twodimensional torus (a closed trajectory in the case of a time-independent perturbation) shrinking to the equilibrium position as the small parameter tends to zero. The proofs use methods of the Krylov-Bogolyubov theory for the case of periodic perturbations or the implicit function theorem for the case of time-independent.

KW - bifurcation

KW - oscillator

KW - velocity-dependent restoring force

KW - periodic perturbations

KW - bifurcation

KW - oscillator

KW - velocity-dependent restoring force

KW - periodic perturbations

UR - http://www.scopus.com/inward/record.url?scp=85073001891&partnerID=8YFLogxK

U2 - 10.1134/S0012266119080020

DO - 10.1134/S0012266119080020

M3 - Article

VL - 55

SP - 1011

EP - 1016

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 8

ER -

ID: 49226112