TY  - JOUR
A1  - Komarov, Maxim
A1  - Pikovskij, Arkadij
T1  - Multiplicity of singular synchronous States in the kuramoto model of coupled oscillators
JF  - Physical review letters
N2  - We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.111.204101
SN  - 0031-9007
SN  - 1079-7114
VL  - 111
IS  - 20
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Komarov, Maxim
A1  - Pikovskij, Arkadij
T1  - Dynamics of multifrequency oscillator communities
JF  - Physical review letters
N2  - We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The simplest situation of three resonantly interacting groups is analyzed in detail. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations and present examples where the interaction between communities leads to their synchrony or to a partially asynchronous state or to a chaotic dynamics of order parameters. DOI: 10.1103/PhysRevLett.110.134101
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.110.134101
SN  - 0031-9007
VL  - 110
IS  - 13
PB  - American Physical Society
CY  - College Park
ER  -