  We consider large rings of weakly-coupled Bose-Einstein condensates,
analyzing their transition to chaotic dynamics and loss of coherence.
Initially, a ring is considered to be in an eigenstate, i.e. in a commensurate
configuration with equal site fillings and equal phase differences between
neighboring sites. Such a ring should exhibit a circulating current whose value
will depend on the initial, non-zero phase difference. The appearance of such
currents is a signature of an established coherence along the ring. If phase
difference falls between $\pi/2$ and $3\pi/2$ and interparticle interaction in
condensates exceeds a critical interaction value $u_c$, the coherence is
supposed to be quickly destroyed because the system enters a chaotic regime due
to inherent instabilities. This is, however, only a part of the story. It turns
out that chaotic dynamics and resulting averaging of circular current to zero
is generally offset by a critical time-scale $t_c$, which is almost two orders
of magnitude larger than the one expected from the linear stability analysis.
We study the critical time-scale in detail in a broad parameter range.
