Radiophysics and Quantum Electronics

, Volume 61, Issue 8–9, pp 672–680 | Cite as

Correlations of the States of Non-Entrained Oscillators in the Kuramoto Ensemble with Noise in the Mean Field

  • A. S. Pikovsky
  • A. V. Dolmatova
  • D. S. GoldobinEmail author

We consider the dynamics of the Kuramoto ensemble oscillators not included in a common synchronized cluster, where the mean field is subject to fluctuations. The fluctuations can be either related to the finite size of the ensemble or superimposed on the mean field in the form of common noise due to the constructive features of the system. It is shown that the states of such oscillators with close natural frequencies appear correlated with each other, since the mean-field fluctuations act as common noise. We quantify the effect with the synchronization index of two oscillators, which is calculated numerically and analytically as a function of the frequency difference and noise intensity. The results are rigorous for large ensembles with additional noise superimposed on the mean field and are qualitatively true for the systems where the mean-field fluctuations are due to the finite size of the ensemble. In the latter case, the effect is found to be independent of the number of oscillators in the ensemble.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. S. Pikovsky
    • 1
    • 2
  • A. V. Dolmatova
    • 3
  • D. S. Goldobin
    • 3
    • 4
    Email author
  1. 1.Potsdam UniversityPotsdamGermany
  2. 2.N. I. Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  3. 3.Institute for Mechanics of Continuous MediaUral Branch of the Russian Academy of SciencesPermRussia
  4. 4.State University of PermPermRussia

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