Mode-locking in systems of globally coupled phase oscillators

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Date
2017
Volume
2418
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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 lasers 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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Keywords
Phase oscillators, mode-locking
Citation
Eydam, S., & Wolfrum, M. (2017). Mode-locking in systems of globally coupled phase oscillators (Vol. 2418). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2418
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