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
JF  - 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
U6  - https://doi.org/10.1007/s11141-019-09927-4
SN  - 0033-8443
SN  - 1573-9120
VL  - 61
IS  - 8-9
SP  - 672
EP  - 680
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Tyulkina, Irina V.
A1  - Goldobin, Denis S.
A1  - Klimenko, Lyudmila S.
A1  - Pikovskij, Arkadij
T1  - Two-Bunch Solutions for the Dynamics of Ott–Antonsen Phase Ensembles
JF  - Radiophysics and Quantum Electronics
N2  - We have developed a method for deriving systems of closed equations for the dynamics of order parameters in the ensembles of phase oscillators. The Ott-Antonsen equation for the complex order parameter is a particular case of such equations. The simplest nontrivial extension of the Ott-Antonsen equation corresponds to two-bunch states of the ensemble. Based on the equations obtained, we study the dynamics of multi-bunch chimera states in coupled Kuramoto-Sakaguchi ensembles. We show an increase in the dimensionality of the system dynamics for two-bunch chimeras in the case of identical phase elements and a transition to one-bunch "Abrams chimeras" for imperfect identity (in the latter case, the one-bunch chimeras become attractive).
Y1  - 2019
U6  - https://doi.org/10.1007/s11141-019-09924-7
SN  - 0033-8443
SN  - 1573-9120
VL  - 61
IS  - 8-9
SP  - 640
EP  - 649
PB  - Springer
CY  - New York
ER  -