Synchronization of noise-induced escape: how it starts and ends (Keynote Address)

We provide a complete solution of the problem of noise-induced escape in periodically driven systems. We show that both the exponent and the prefactor in the escape rate display scaling behavior with the field intensity. The corresponding scaling is related to synchronization of escape events by the modulating field. The onset of the synchronization with the increasing field and its loss as the field approaches a bifurcational value lead to a strongly nonmonotonic field dependence of the prefactor.