WIAS Preprint No. 2234, (2016)

Is there an impact of small phase lags in the Kuramoto model?



Authors

  • Omel'chenko, Oleh
    ORCID: 0000-0003-0526-1878
  • Wolfrum, Matthias

2010 Mathematics Subject Classification

  • 34C15 37N20 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt, 89.75.Kd

Keywords

  • coupled oscillators, synchronization transition, Kuramoto model

Abstract

We discuss the influence of small phase lags on the synchronization transitions in the Kuramoto model for a large inhomogeneous population of globally coupled phase oscillators. Without a phase lag, all unimodal distributions of the natural frequencies give rise to a classical synchronization scenario, where above the onset of synchrony at the Kuramoto threshold there is an increasing synchrony for increasing coupling strength. We show that already for arbitrarily small phase lags there are certain unimodal distributions of natural frequencies such that for increasing coupling strength synchrony may decrease and even complete incoherence may regain stability. Moreover, our example allows a qualitative understanding of the mechanism for such non-universal synchronization transitions.

Appeared in

  • Chaos, 26 (2016) pp. 094806/1--094806/6.

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