  We study the nature of the synchronization transition in spatially extended
systems by discussing a simple stochastic model. An analytic argument is put
forward showing that, in the limit of discontinuous processes, the transition
belongs to the directed percolation (DP) universality class. The analysis is
complemented by a detailed investigation of the dependence of the first passage
time for the amplitude of the difference field on the adopted threshold. We
find the existence of a critical threshold separating the regime controlled by
linear mechanisms from that controlled by collective phenomena. As a result of
this analysis we conclude that the synchronization transition belongs to the DP
class also in continuous models. The conclusions are supported by numerical
checks on coupled map lattices too.
