Chimera states in heterogeneous networks

Chimera states in networks of coupled oscillators occur when some fraction of the oscillators synchronize with one another, while the remaining oscillators are incoherent. Several groups have studied chimerae in networks of identical oscillators, but here we study these states in heterogeneous models for which the natural frequencies of the oscillators are chosen from a distribution. For a model consisting of two subnetworks, we obtain exact results by reduction to a finite set of differential equations, and for a network of oscillators in a ring, we generalize known results. We find that heterogeneity can destroy chimerae, destroy all states except chimerae, or destabilize chimerae in Hopf bifurcations, depending on the form of the heterogeneity.