  We investigate the phenomenon of chaos synchronization in systems subject to
coexisting autonomous and external global fields by employing a simple model of
coupled maps. Two states of chaos synchronization are found: (i) complete
synchronization, where the maps synchronize among themselves and to the
external field, and (ii) generalized or internal synchronization, where the
maps synchronize among themselves but not to the external global field. We show
that the stability conditions for both states can be achieved for a system of
minimum size of two maps. We consider local maps possessing robust chaos and
characterize the synchronization states on the space of parameters of the
system. The state of generalized synchronization of chaos arises even the drive
and the local maps have the same functional form. This behavior is similar to
the process of spontaneous ordering against an external field found in
nonequilibrium systems.
