  Kuramoto oscillators have been proposed earlier as a model for interacting
systems that exhibit synchronisation. In this article we study the difference
between networks with symmetric and asymmetric distribution of natural
frequencies. We first indicate that the synchronisation frequency of the
oscillators is independent of the natural frequency distribution for a
completely connected network. Further we analyse the case of oscillators in a
directed ring-network where asymmetry in the natural frequency distribution is
seen to shift the synchronisation frequency of the network. We also present an
estimate of the shift in the frequencies for slightly asymmetric distributions.

Adaptation and Self-Organizing Systems