Alessandro Scirè, Pere Colet,  and Maxi San Miguel
Instituto Mediterràneo de Estudios Avanzados (IMEDEA), CSIC-UIB
 

We analyze a  system of globally coupled limit-cycle oscillators, considering the polarization degree of freedom (vectorial oscillators); including randomly distributed natural frequencies and oscillation angles.
Increasing the coupling, no polarization order enhancement is possible until the phases start to synchronize, because the phase disorder destroys the interaction among the polarization variables. For strong natural angle disorder, the phases synchronize first, and polarization synchrony takes place at a higher coupling level, through a partial de-synchronization of the phases. We developed an approximated theory to estimate the phase and polarization order parameters. For weak natural angle disorder, the two transitions merge in a unique process to full synchrony, and we have provided the critical coupling for its onset.