  This paper deals with adaptive synchronization of chaos in the presence of
time-varying communication-delays. We consider two bidirectionally coupled
systems that seek to synchronize through a signal that each system sends to the
other one and is transmitted with an unknown time-varying delay. We show that
an appropriate adaptive strategy can be devised that is successful in
dynamically identifying the time-varying delay and in synchronizing the two
systems. The performance of our strategy with respect to the choice of the
initial conditions and the presence of noise in the communication channels is
tested by using numerical simulations. Another advantage of our approach is
that in addition to estimating the communication-delay, the adaptive strategy
could be used to simultaneously identify other parameters, such as e.g., the
unknown time-varying amplitude of the received signal.
