  We study the population dynamics of a ring-shaped optical lattice with a high
number of particles per site and a low, below ten, number of wells. Using a
localized on-site basis defined in terms of stationary states, we were able to
construct a multiple-mode model depending on relevant hopping and on-site
energy parameters. We show that in case of two wells, our model corresponds
exactly to the latest improvement of the two-mode model. We derive a formula
for the self-trapping period, which turns out to be chiefly ruled by the
on-site interaction energy parameter. By comparing to time dependent
Gross-Pitaevskii simulations, we show that the multimode model results can be
enhanced in a remarkable way over all the regimes by only renormalizing such a
parameter. Finally, using a different approach which involves only the ground
state density, we derive an effective interaction energy parameter that shows
to be in accordance with the renormalized one.
