Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
arXiv:1007.4382 · doi:10.1063/1.3491344
Abstract
We theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective phase equations describing the macroscopic rhythms of the groups from microscopic Langevin phase equations of the individual oscillators via nonlinear Fokker-Planck equations. For sinusoidal microscopic coupling, we determine the type of the collective phase coupling function, i.e., whether the groups exhibit in-phase or anti-phase synchronization. We show that the macroscopic rhythms can exhibit effective anti-phase synchronization even if the microscopic phase coupling between the groups is in-phase, and vice versa. Moreover, near the onset of collective oscillations, we analytically obtain the collective phase coupling function using center-manifold and phase reductions of the nonlinear Fokker-Planck equations.
15 pages, 7 figures
References in corpus (10)
- Synchronization in complex networks
- Critical phenomena in complex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
- Collective Phase Sensitivity
- Noise-induced Turbulence in Nonlocally Coupled Oscillators
- Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
- Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing
- Asymmetry--induced effects in coupled phase oscillator ensembles: Routes to synchronization
- Routes to synchrony between asymmetrically interacting oscillator ensembles