TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Dolmatova, A.
A1  - Goldobin, Denis S.
T1  - Correlations of the States of Non-Entrained Oscillators in the Kuramoto Ensemble with Noise in the Mean Field
T2  - Radiophysics and Quantum Electronics
N2  - 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.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/50726
SN  - 0033-8443
SN  - 1573-9120
VL  - 61
IS  - 8-9
SP  - 672
EP  - 680
PB  - Springer
CY  - New York
ER  -