The synchronized spinor exciton-polariton condensate is derived for the symmetric and asymmetric pump configurations.

For a small Zeeman splitting, the two condensates are synchronized as an elliptically polarized condensate.

For a larger Zeeman splitting, these two condensates behave as two circularly-polarized components.

The self-interaction dominates the synchronization, and a minimum flipping rate is required to reach the synchronization.