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

Yu. N. Bibikov, V. R. Bukaty

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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.
Original languageEnglish
Pages (from-to)1011-1016
JournalDifferential Equations
Volume55
Issue number8
StatePublished - 28 Aug 2019

Scopus subject areas

  • Mathematics(all)

Keywords

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

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