TY  - JOUR
A1  - Baibolatov, Yernur
A1  - Rosenblum, Michael
A1  - Zhanabaev, Zeinulla Zh.
A1  - Pikovskij, Arkadij
T1  - Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling
N2  - We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically (i) states of complete synchrony, (ii) regimes with coexistence of a synchronous cluster and a drifting subpopulation, and (iii) self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.82.016212
SN  - 1539-3755
ER  -