title: Phase synchronization and polarization ordering of globally coupled oscillators.
abstract: 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 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 cannot take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results.
authors.affiliation: Instituto Mediterráneo de Estudios Avanzados, IMEDEA (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain. scire@imedea.uib.es
authors.forename: Alessandro
authors.initials: A
authors.lastname: Scirè
authors.forename: Pere
authors.initials: P
authors.lastname: Colet
authors.forename: Maxi
authors.initials: M
authors.lastname: San Miguel