  We investigate synchronization between two unidirectionally linearly coupled
chaotic non-identical time-delayed systems and show that parameter mismatches
are of crucial importance to achieve synchronization. We establish that
independent of the relation between the delay time in the coupled systems and
the coupling delay time, only retarded synchronization with the coupling delay
time is obtained. We show that with parameter mismatch or without it neither
complete nor anticipating synchronization occurs. We derive existence and
stability conditions for the retarded synchronization manifold. We demonstrate
our approach using examples of the Ikeda and Mackey-Glass models. Also for the
first time we investigate chaos synchronization in time-delayed systems with
variable delay time and find both existence and sufficient stability conditions
for the retarded synchronization manifold with the coupling delay lag time.
Also for the first time we consider synchronization between two
unidirectionally coupled chaotic multi-feedback Ikeda systems and derive
existence and stability conditions for the different anticipating, lag, and
complete synchronization regimes.
