Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
arXiv:1007.5161 · doi:10.1063/1.3491346
Abstract
Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. Coupled amplitude equations describing the collective oscillations of the oscillator groups are obtained by using the Ott-Antonsen ansatz, and then coupled phase equations for the collective oscillations are derived by phase reduction of the amplitude equations. The collective phase coupling function, which determines the dynamics of macroscopic phase differences between the groups, is calculated analytically. It is demonstrated that the groups can exhibit effective anti-phase collective synchronization even if the microscopic external coupling between individual oscillator pairs belonging to different groups is in-phase, and similarly effective in-phase collective synchronization in spite of microscopic anti-phase external coupling between the groups.
11 pages, 3 figures
References in corpus (23)
- Synchronization in complex networks
- Critical phenomena in complex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Chimera states in heterogeneous networks
- Stability diagram for the forced Kuramoto model
- Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
- The Spectrum of the Partially Locked State for the Kuramoto Model
- Collective Phase Sensitivity
- Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
- Invariant submanifold for series arrays of Josephson junctions
- Phase Response Curves of Coupled Oscillators
- Noise-induced Turbulence in Nonlocally Coupled Oscillators
- Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing
- Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
- Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses
- Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
- Impact of hierarchical modular structure on ranking of individual nodes in directed networks
- Asymmetry--induced effects in coupled phase oscillator ensembles: Routes to synchronization
- Analysis of relative influence of nodes in directed networks
- Routes to synchrony between asymmetrically interacting oscillator ensembles
- Perturbation Analysis of Complete Synchronization in Networks of Phase Oscillators