  We consider a polariton condensate in a microcavity driven by a bichromatic
resonant pump formed by two vortical laser beams carrying different topological
charges. The system is additionally confined in a ring-shaped potential. We
show that in this system steadily rotating nonlinear localized modes can be
excited, whose angular rotation frequency is determined by optical frequencies
and topological charges of the pump beams. When pump frequencies approach
eigenfrequencies of the modes of the ring potential, resonant growth of peak
amplitude of the excited states occurs. Repulsive polariton-polariton
interactions lead to tilting of the resonance curves and appearance of
bistability of rotating patterns.
