  We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of
identical coupled phase oscilla- tors with various kinds of time-dependent
connectivity using Eulerian discretization. We first explore the parameter
spaces for various types of collective states using the phase plots of the two
statistical quantities, namely the strength of incoherence and the discontinity
measure. In the quasi-static limit of the changing of coupling range, we have
observed how the system relaxes from one state to another and have identified a
few interesting collective dynamical states along the way. Under a sinusoidal
change of the coupling range, the global order parameter characterizing the
degree of synchronization in the system is shown to undergo a hysteresis with
the coupling range. Finally, we study the low-dimensional spatio-temporal
dynamics of the local order parameter in the continuum limit using the
recently-developed Ott-Antonsen ansatz and justify some of our numerical
results. In particular, we identify an intrinsic time-scale of the Kuramoto
system and show that the simulations exhibit two distinct kinds of qualitative
behavior in two cases when the time-scale associated with the switching of the
coupling radius is very large compared to the intrinsic time-scale and when it
is comparable with the intrinsic time-scale.
