  It is shown that the synchronization behavior of a system of chaotic maps
subject to either an external forcing or a coupling function of their internal
variables can be inferred from the behavior of a single element in the system,
which can be seen as a single drive-response map. From the conditions for
stable synchronization in this single driven-map model with minimal
ingredients, we find minimal conditions for the emergence of complete and
generalized chaos synchronization in both driven and autonomous associated
systems. Our results show that the presence of a common drive or a coupling
function for all times is not indispensable for reaching synchronization in a
system of chaotic oscillators, nor is the simultaneous sharing of a field,
either external or endogenous, by all the elements. In the case of an
autonomous system, the coupling function does not need to depend on all the
internal variables for achieving synchronization and its functional form is not
crucial for generalized synchronization. What becomes essential for reaching
synchronization in an extended system is the sharing of some minimal
information by its elements, on the average, over long times, independently of
the nature (external or internal) of its source.

Chaotic Dynamics