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We analyze repulsively coupled Kuramoto oscillators, which are exposed to adistribution of natural frequencies. This source of disorder leads to closedorbits with a variety of different periods, which can be orders of magnitudelonger than periods of individual oscillators. By construction the attractorspace is quite rich. This may cause long transients until the deterministictrajectories find their stationary orbits. The smaller the width of thedistribution about the common natural frequency is, the longer are the emergingtime scales on average. Among the long-period orbits we find self-similarsequences of temporary phase-locked motion on different time scales. The ratioof time scales is determined by the ratio of widths of the distributions.

Emerging long orbits and self-similar temporal sequences in classical oscillators