  We study synchronization patterns in repulsively coupled Kuramoto oscillators
and focus on the impact of disorder in the natural frequencies. Among other
choices we select the grid size and topology in a way that we observe a
dynamically induced dimensional reduction with a continuum of attractors as
long as the natural frequencies are uniformly chosen. When we introduce
disorder in these frequencies, we find limit cycles with periods that are
orders of magnitude longer than the natural frequencies of individual
oscillators. Moreover we identify sequences of temporary patterns of
phase-locked motion, which are self-similar in time and whose periods scale
with a power of the inverse width about a uniform frequency distribution. This
behavior provides challenges for future research.
