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We study synchronization patterns in repulsively coupled Kuramoto oscillatorsand focus on the impact of disorder in the natural frequencies. Among otherchoices we select the grid size and topology in a way that we observe adynamically induced dimensional reduction with a continuum of attractors aslong as the natural frequencies are uniformly chosen. When we introducedisorder in these frequencies, we find limit cycles with periods that areorders of magnitude longer than the natural frequencies of individualoscillators. Moreover we identify sequences of temporary patterns ofphase-locked motion, which are self-similar in time and whose periods scalewith a power of the inverse width about a uniform frequency distribution. Thisbehavior provides challenges for future research.

Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators