  We examine the design of the entrainment process for an uncountably infinite
collection of coupled phase oscillators that are all subject to the same
periodic driving signal. In the absence of coupling, an appropriately designed
input can result in each oscillator attaining the frequency of the driving
signal, with a phase offset determined by its natural frequency. We consider a
special case of interacting oscillators in which the coupling tends to
destabilize the phase configuration to which the driving signal would send the
collection in the absence of coupling. In this setting we derive stability
results that characterize the trade-off between the effects of driving and
coupling, and compare these results to the well-known Kuramoto model of a
collection of free-running coupled oscillators.
