  We analyze the behavior of the first few cumulant in an array with a small
number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf
19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global
coupling and derived an infinite hierarchy of differential equations for the
cumulant moments. They focused on the behavior of infinite size systems using a
strategy based on truncating the hierarchy. In this work we explore the
reliability of such an approach to describe systems with a small number of
elements. We carry out an extensive numerical analysis of the truncated
hierarchy as well as numerical simulations of the full set of Langevin
equations governing the dynamics. We find that the results provided by the
truncated hierarchy for finite systems are at variance with those of the
Langevin simulations for large regions of parameter space. The truncation of
the hierarchy leads to a dependence on initial conditions and to the
coexistence of states which are not consistent with the theoretical
expectations based on the multidimensional linear Fokker-Planck equation for
finite arrays.
