  We investigate the problem of vortex trapping in cyclically coupled
Bose-Josephson junctions. Starting with $N$ independent BECs we couple the
condensates through Josephson links and allow the system to reach a stable
circulation by adding a dissipative term in our semiclassical equations of
motion. The central question we address is what is the probability to trap a
vortex with winding number $m$. Our numerical simulations reveal that the final
distribution of winding numbers is narrower than the initial distribution of
total phases, indicating an increased probability for no-vortex configurations.
Further, the nonlinearity of the problem manifests itself in the somewhat
counter-intuitive result that it is possible to obtain a non-zero circulation
starting with zero total phase around the loop. The final width of the
distribution of winding numbers for $N$ sites scales as $\lambda N^{\alpha}$,
where $\alpha=0.47\pm 0.01$ and $\lambda <0.67$ (value predicted for the
initial distribution) indicating a shrinking of the final distribution. The
actual value of $\lambda$ is found to depend on the strength of dissipation.
