  Frequency desynchronized attractors cannot appear in identically coupled
symmetric phase oscillators because "overtaking" of phases cannot occur. This
restriction no longer applies for more general identically coupled oscillators.
Hence, it is interesting to understand precisely how frequency synchrony is
lost and how invariant sets such as attracting weak chimeras are generated at
torus breakup, where the phase description breaks down. Maistrenko et al (2016)
found numerical evidence of an organizing center for weak chimeras in a system
of $N=3$ coupled identical Kuramoto oscillators with inertia. This paper
identifies this organizing center and shows that it corresponds to a particular
type of non-transverse heteroclinic bifurcation that is generic in the context
of symmetry. At this codimension two bifurcation there is a splitting of
connecting orbits between the in-phase (fully synchronized) state. This
generates a wide variety of associated bifurcations to weak chimeras. We
further highlight a second organizing center associated with a codimension two
symmetry-breaking heteroclinic connection.
