  We study the response of one dimensional diffusive systems, consisting of
particles interacting via symmetric or asymmetric exclusion, to time-periodic
driving from two reservoirs coupled to the ends. The dynamical response of the
system can be characterized in terms of the structure factor. We find an
interesting frequency dependent response -- the current carrying majority
excitons cyclically crosses over from a short wavelength mode to a long
wavelength mode with an intermediate regime of coexistence. This effect being
boundary driven, decays inversely with system size. Analytic calculations show
that this behavior is common to diffusive systems, both in absence and presence
of correlations.
