  Chimera states are complex spatio-temporal patterns that consist of
coexisting domains of spatially coherent and incoherent dynamics. This
counterintuitive phenomenon was first observed in systems of identical
oscillators with symmetric coupling topology. Can one overcome these
limitations? To address this question, we discuss the robustness of chimera
states in networks of FitzHugh-Nagumo oscillators. Considering networks of
inhomogeneous elements with regular coupling topology, and networks of
identical elements with irregular coupling topologies, we demonstrate that
chimera states are robust with respect to these perturbations, and analyze
their properties as the inhomogeneities increase. We find that modifications of
coupling topologies cause qualitative changes of chimera states: additional
random links induce a shift of the stability regions in the system parameter
plane, gaps in the connectivity matrix result in a change of the multiplicity
of incoherent regions of the chimera state, and hierarchical geometry in the
connectivity matrix induces nested coherent and incoherent regions.
