  Chimera states are dynamical patterns in networks of coupled oscillators in
which regions of synchronous and asynchronous oscillation coexist. Although
these states are typically observed in large ensembles of oscillators and
analyzed in the continuum limit, chimeras may also occur in systems with finite
(and small) numbers of oscillators. Focusing on networks of $2N$ phase
oscillators that are organized in two groups, we find that chimera states,
corresponding to attracting periodic orbits, appear with as few as two
oscillators per group and demonstrate that for $N>2$ the bifurcations that
create them are analogous to those observed in the continuum limit. These
findings suggest that chimeras, which bear striking similarities to dynamical
patterns in nature, are observable and robust in small networks that are
relevant to a variety of real-world systems.
