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Phase Synchronization and Polarization Ordering of Globally Coupled Oscillators

A.Scirè; P.Colet; M. San Miguel
Physical Review E 70, 035201(R) (1-4) (2004)

We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and a polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement can not take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results.