  We show that the synchronized states of two systems of identical chaotic maps
subject to either, a common drive that acts with a probability p in time or to
the same drive acting on a fraction p of the maps, are similar. The
synchronization behavior of both systems can be inferred by considering the
dynamics of a single chaotic map driven with a probability p. The synchronized
states for these systems are characterized on their common space of parameters.
Our results show that the presence of a common external drive for all times is
not essential for reaching synchronization in a system of chaotic oscillators,
nor is the simultaneous sharing of the drive by all the elements in the system.
Rather, a crucial condition for achieving synchronization is the sharing of
some minimal, average information by the elements in the system over long
times.
