  By using a semi-analytical dynamical mean-field approximation previously
proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we
have studied the synchronization of stochastic, small-world (SW) networks of
FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity
between results for {\it diffusive} and {\it sigmoid} couplings have been
discussed. It has been shown that with introducing the weak heterogeneity to
regular networks, the synchronization may be slightly increased for diffusive
couplings, while it is decreased for sigmoid couplings. This increase in the
synchronization for diffusive couplings is shown to be due to their local,
negative feedback contributions, but not due to the shorten average distance in
SW networks. Synchronization of SW networks depends not only on their structure
but also on the type of couplings.
