  The transition to turbulence via spatiotemporal intermittency is investigated
in the context of coupled maps defined on small-world networks. The local
dynamics is given by the Chat\'e-Manneville minimal map previously used in
studies of spatiotemporal intermittency in ordered lattices. The critical
boundary separating laminar and turbulent regimes is calculated on the
parameter space of the system, given by the coupling strength and the rewiring
probability of the network. Windows of relaminarization are present in some
regions of the parameter space. New features arise in small-world networks; for
instance, the character of the transition to turbulence changes from second
order to a first order phase transition at some critical value of the rewiring
probability. A linear relation characterizing the change in the order of the
phase transition is found. The global quantity used as order parameter for the
transition also exhibits nontrivial collective behavior for some values of the
parameters. These models may describe several processes occurring in nonuniform
media where the degree of disorder can be continuously varied through a
parameter.
