  We suggest a definition for a type of chimera state that appears in networks
of indistinguishable phase oscillators. Defining a "weak chimera" as a type of
invariant set showing partial frequency synchronization, we show that this
means they cannot appear in phase oscillator networks that are either globally
coupled or too small. We exhibit various networks of four, six and ten
indistinguishable oscillators where weak chimeras exist with various dynamics
and stabilities. We examine the role of Kuramoto-Sakaguchi coupling in giving
degenerate (neutrally stable) families of weak chimera states in these example
networks.
