  As exemplified by the Kuramoto model, large systems of coupled oscillators
may undergo a transition to phase coherence with increasing coupling strength.
It is shown that below the critical coupling strength for this transition such
systems may be expected to exhibit `echo' phenomena: a stimulation by two
successive pulses separated by a time interval tau leads to the spontaneous
formation of response pulses at a time tau, 2 tau, 3 tau ..., after the second
stimulus pulse. Analysis of this phenomenon, as well as illustrative numerical
experiments, are presented. The theoretical significance and potential uses of
echoes in such systems are discussed.

Chaotic Dynamics