  We consider the approximations behind the typical mean-field model derived
for a class of systems made up of type II excitable units influenced by noise
and coupling delays. The formulation of the two approximations, referred to as
the Gaussian and the quasi-independence approximation, as well as the fashion
in which their validity is verified, are adapted to reflect the essential
properties of the underlying system. It is demonstrated that the failure of the
mean-field model associated with the breakdown of the quasi-independence
approximation can be predicted by the noise-induced bistability in the dynamics
of the mean-field system. As for the Gaussian approximation, its violation is
related to the increase of noise intensity, but the actual condition for
failure can be cast in qualitative, rather than quantitative terms. We also
discuss how the fulfilment of the mean-field approximations affects the
statistics of the first return times for the local and global variables,
further exploring the link between the fulfilment of the quasi-independence
approximation and certain forms of synchronization between the individual
units.
