  Interaction within an ensemble of coupled nonlinear oscillators induces a
variety of collective behaviors. One of the most fascinating is a chimera state
which manifests the coexistence of spatially distinct populations of coherent
and incoherent elements. Understanding of the emergent chimera behavior in
controlled experiments or real systems requires a focus on the consideration of
heterogeneous network models. In this study, we explore the transitions in a
heterogeneous Kuramoto model under the monotonical increase of the coupling
strength and specifically find that this system exhibits a frequency-modulated
chimera-like pattern during the explosive transition to synchronization. We
demonstrate that this specific dynamical regime originates from the interplay
between (the evolved) attractively and repulsively coupled subpopulations. We
also show that the above mentioned chimera-like state is induced under weakly
non-local, small-world and sparse scale-free coupling and suppressed in
globally coupled, strongly rewired and dense scale-free networks due to the
emergence of the large-scale connections.
