Natural Ordering and Uniform Tidal Effects in Globally Coupled Phase Oscillator Models

Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the internal structure of coherent subsets of oscillators can be made based on the observations of natural ordering and uniform tidal effects. The approximation is seen to perform well for predicting the microstructure in a variety of phase oscillator models.