WIAS Preprint No. 2418, (2017)

Mode-locking in systems of globally coupled phase oscillators



Authors

  • Eydam, Sebastian
  • Wolfrum, Matthias

2010 Mathematics Subject Classification

  • 34C15 37N20

2008 Physics and Astronomy Classification Scheme

  • 89.75.-k 42.60.Fc 05.45Xt 05.45.-a

Keywords

  • Phase oscillators, mode-locking

DOI

10.20347/WIAS.PREPRINT.2418

Abstract

We investigate the dynamics of a Kuramoto-type system of globally coupled phase oscillators with equidistant natural frequencies and a coupling strength below the synchronization threshold. It turns out that in such cases one can observe a stable regime of sharp pulses in the mean field amplitude with a pulsation frequency given by spacing of the natural frequencies. This resembles a process known as mode-locking in laser and relies on the emergence of a phase relation induced by the nonlinear coupling. We discuss the role of the first and second harmonic in the phase-interaction function for the stability of the pulsations and present various bifurcating dynamical regimes such as periodically and chaotically modulated mode-locking, transitions to phase turbulence and intermittency. Moreover, we study the role of the system size and show that in certain cases one can observe type-II supertransients, where the system reaches the globally stable mode-locking solution only after an exponentially long transient of phase turbulence.

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