Bifurcation of an Oscillatory Mode under a Periodic Perturbation of a Special Oscillator

Результат исследований: Научные публикации в периодических изданияхстатья

1 цитирование (Scopus)

Выдержка

We study a bifurcation from the zero solution of the differential equation ẍ + xp/q = 0, where p > q > 1 are odd coprime numbers, under periodic (in particular, time-invariant) perturbations depending on a small positive parameter ε. The motion separation method is used to derive the bifurcation equation. To each positive root of this equation, there corresponds an invariant two-dimensional torus (a closed trajectory in the time-invariant case) shrinking to the equilibrium position x = 0 as ε → 0. The proofs use methods of the Krylov-Bogolyubov theory to study time-periodic perturbations and the implicit function theorem in the case of time-invari ant perturbations.

Язык оригиналаанглийский
Страницы (с-по)753-757
ЖурналDifferential Equations
Том55
Номер выпуска6
Ранняя дата в режиме онлайн15 июл 2019
DOI
СостояниеОпубликовано - 2019

Отпечаток

Bifurcation
Perturbation
Invariant
Implicit Function Theorem
Coprime
Shrinking
Torus
Odd
Roots
Trajectory
Differential equation
Closed
Motion
Zero

Предметные области Scopus

  • Анализ
  • Математика (все)

Цитировать

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Bifurcation of an Oscillatory Mode under a Periodic Perturbation of a Special Oscillator. / Bibikov, Yu. N.; Bukaty, V. R.

В: Differential Equations, Том 55, № 6, 2019, стр. 753-757.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Bifurcation of an Oscillatory Mode under a Periodic Perturbation of a Special Oscillator

AU - Bibikov, Yu. N.

AU - Bukaty, V. R.

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PY - 2019

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AB - We study a bifurcation from the zero solution of the differential equation ẍ + xp/q = 0, where p > q > 1 are odd coprime numbers, under periodic (in particular, time-invariant) perturbations depending on a small positive parameter ε. The motion separation method is used to derive the bifurcation equation. To each positive root of this equation, there corresponds an invariant two-dimensional torus (a closed trajectory in the time-invariant case) shrinking to the equilibrium position x = 0 as ε → 0. The proofs use methods of the Krylov-Bogolyubov theory to study time-periodic perturbations and the implicit function theorem in the case of time-invari ant perturbations.

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