  Chimera states in networks of coupled oscillators occur when some fraction of
the oscillators synchronise with one another, while the remaining oscillators
are incoherent. Several groups have studied chimerae in networks of identical
oscillators, but here we study these states in a heterogeneous model for which
the natural frequencies of the oscillators are chosen from a distribution. We
obtain exact results by reduction to a finite set of differential equations. We
find that heterogeneity can destroy chimerae, destroy all states except
chimerae, or destabilise chimerae in Hopf bifurcations, depending on the form
of the heterogeneity.
