  We present study of the dynamics of two ring waveguide structure with space
dependent coupling, linear gain and nonlinear absorption - the system that can
be implemented in polariton condensates, optical waveguides, and nanocavities.
We show that by turning on and off local coupling between rings one can
selectively generate permanent vortex in one of the rings. We find that due to
the modulation instability it is also possible to observe several complex
nonlinear phenomena, including spontaneous symmetry breaking, stable
inhomogeneous states with interesting structure of currents flowing between
rings, generation of stable symmetric and asymmetric circular flows with
various vorticities, etc. The latter can be created in pairs (for relatively
narrow coupling length) or as single vortex in one of the channels, that is
later alternating between channels.
