  A system's response to external periodic changes can provide crucial
information about its dynamical properties. We investigate the synchronization
transition, an archetypical example of a dynamic phase transition, in the
framework of such a temporal response. The Kuramoto model under periodically
switching interactions has the same type of phase transition as the original
mean-field model. Furthermore, we see that the signature of the synchronization
transition appears in the relative delay of the order parameter with respect to
the phase of oscillating interactions as well. Specifically, the phase shift
becomes significantly larger as the system gets closer to the phase transition
so that the order parameter at the minimum interaction density can even be
larger than that at the maximum interaction density, counterintuitively. We
argue that this phase-shift inversion is caused by the diverging relaxation
time, in a similar way to the resonance near the critical point in the kinetic
Ising model. Our result, based on exhaustive simulations on globally coupled
systems as well as scale-free networks, shows that an oscillator system's phase
transition can be manifested in the temporal response to the topological
dynamics of the underlying connection structure.
