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

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.
Язык оригиналаанглийский
Страницы (с-по)1011-1016
ЖурналDifferential Equations
Том55
Номер выпуска8
СостояниеОпубликовано - 28 авг 2019

Отпечаток

Bifurcation
Perturbation
Dependent
Implicit Function Theorem
Separation of Variables
Shrinking
Small Parameter
Torus
Roots
Tend
Trajectory
Closed
Invariant
Motion
Zero

Предметные области Scopus

  • Математика (все)

Ключевые слова

  • bifurcation
  • oscillator
  • velocity-dependent restoring force
  • periodic perturbations

Цитировать

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

В: Differential Equations, Том 55, № 8, 28.08.2019, стр. 1011-1016.

Результат исследований: Научные публикации в периодических изданияхстатья

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 - 2019/8/28

Y1 - 2019/8/28

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

M3 - Article

VL - 55

SP - 1011

EP - 1016

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 8

ER -