  In a network of coupled oscillators, a symmetry-broken dynamical state
characterized by the coexistence of coherent and incoherent parts can
spontaneously form. It is known as a chimera state. We study chimera states in
a network consisting of six populations of identical Kuramoto-Sakaguchi phase
oscillators. The populations are arranged in a ring and oscillators belonging
to one population are uniformly coupled to all oscillators within the same
population and to those in the two neighboring populations. This topology
supports the existence of different configurations of coherent and incoherent
populations along the ring, but all of them are linearly unstable in most of
the parameter space. Yet, chimera dynamics is observed from random initial
conditions in a wide parameter range, characterized by one incoherent and five
synchronized populations. These observable states are connected to the
formation of a heteroclinic cycle between symmetric variants of saddle
chimeras, which gives rise to a switching dynamics. We analyze the dynamical
and spectral properties of the chimeras in the thermodynamic limit using the
Ott-Antonsen ansatz, and in finite-sized systems employing Watanabe-Strogatz
reduction. For a heterogeneous frequency distribution, a small heterogeneity
renders a heteroclinic switching dynamics asymptotically attracting. However,
for a large heterogeneity, the heteroclinic orbit does not survive; instead, it
is replaced by a variety of attracting chimera states.
