Characterization of chimeras in coupled phase oscillators based on a coherence function (Q2108665)

The authors study a ring of Kuramoto phase oscillators with nonlocal coupling which decays exponentially with the distance between oscillators. The oscillators' intrinsic frequencies are randomly chosen from a unit Gaussian distribution. For different values of the overall coupling strength and the spatial scale of coupling, states labelled ``coherent'', ``chimera'', and ``completely incoherent'' are observed. They measure a spatial correlation function for each of these states. They then introduce a scalar measure which determines what fraction of the oscillators are in a coherent state (neighbouring oscillators have similar phases) as opposed to incoherent (neighbouring oscillators have very different phases). This scalar varies as expected as parameters are varied.