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Kuramoto oscillators have been proposed earlier as a model for interactingsystems that exhibit synchronisation. In this article we study the differencebetween networks with symmetric and asymmetric distribution of naturalfrequencies. We first indicate that the synchronisation frequency of theoscillators is independent of the natural frequency distribution for acompletely connected network. Further we analyse the case of oscillators in adirected ring-network where asymmetry in the natural frequency distribution isseen to shift the synchronisation frequency of the network. We also present anestimate of the shift in the frequencies for slightly asymmetric distributions.

Dependence of synchronisation frequency of Kuramoto oscillators on symmetry of natural frequency distribution