  Networks of identical, symmetrically coupled oscillators can spontaneously
split into synchronized and desynchronized sub-populations. Such chimera states
were discovered in 2002, but are not well understood theoretically. Here we
obtain the first exact results about the stability, dynamics, and bifurcations
of chimera states by analyzing a minimal model consisting of two interacting
populations of oscillators. Along with a completely synchronous state, the
system displays stable chimeras, breathing chimeras, and saddle-node, Hopf and
homoclinic bifurcations of chimeras.
