Parametrically modulated oscillator dimer: An analytic solution

Academic Article

Abstract

  • A dimer consisting of two coupled oscillators undergoing periodic parametric modulations with a phase difference θ reveals a rich panorama of stability-instability boundaries as a function of the system parameters. It was recently established that the instabilities observed in such dimers with a phase difference θ = 0 and with a phase difference θ = π qualitatively and even quantitatively capture a great deal of the behavior of a mean field model of coupled parametric oscillators with random phases that undergo collective parametric instabilities. These similarities were established numerically for lack of an analytic solution for the θ = π dimer. Herein we present an analytic solution for such a parametrically modulated dimer. We present the exact associated instability boundaries and thus improve on earlier ones generated by numerical simulations. © 2002 Elsevier Science B.V. All rights reserved.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Kawai R; Lindenberg K; Van Den Broeck C
  • Start Page

  • 119
  • End Page

  • 140
  • Volume

  • 312
  • Issue

  • 1-2