  We consider a ring of identical or near identical coupled periodic
oscillators in which the connections have randomly heterogeneous strength. We
use the master stability function method to determine the possible patterns at
the desynchronization transition that occurs as the coupling strengths are
increased. We demonstrate Anderson localization of the modes of instability,
and show that such localized instability generates waves of desynchronization
that spread to the whole array. Similar results should apply to other networks
with regular topology and heterogeneous connection strengths.
