  We analyzed the localized charge dynamics in the system of $N$ interacting
single-level quantum dots (QDs) coupled to the continuous spectrum states in
the presence of Coulomb interaction between electrons within the dots.
Different dots geometry and initial charge configurations were considered. The
analysis was performed by means of Heisenberg equations for localized electrons
pair correlators.
  We revealed that charge trapping takes place for a wide range of system
parameters and we suggested the QDs geometry for experimental observations of
this phenomenon. We demonstrated significant suppression of Coulomb
correlations with the increasing of QDs number. We found the appearance of
several time scales with the strongly different relaxation rates for a wide
range of the Coulomb interaction values.
