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Interaction within an ensemble of coupled nonlinear oscillators induces avariety of collective behaviors. One of the most fascinating is a chimera statewhich manifests the coexistence of spatially distinct populations of coherentand incoherent elements. Understanding of the emergent chimera behavior incontrolled experiments or real systems requires a focus on the consideration ofheterogeneous network models. In this study, we explore the transitions in aheterogeneous Kuramoto model under the monotonical increase of the couplingstrength and specifically find that this system exhibits a frequency-modulatedchimera-like pattern during the explosive transition to synchronization. Wedemonstrate that this specific dynamical regime originates from the interplaybetween (the evolved) attractively and repulsively coupled subpopulations. Wealso show that the above mentioned chimera-like state is induced under weaklynon-local, small-world and sparse scale-free coupling and suppressed inglobally coupled, strongly rewired and dense scale-free networks due to theemergence of the large-scale connections.

Chimera-like behavior in a heterogeneous Kuramoto model: the interplay between the attractive and repulsive coupling