Heterogeneity induces emergent functional networks for synchronization.

We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We demonstrate that increasing heterogeneity among the nodes in state-dependent networks of phase oscillators causes a differentiation in the activation probabilities of the links when a distributed local network adaptation strategy is used in an evolutionary manner. This, in turn, yields the formation of hubs associated to nodes with larger distances from the average frequency of the ensemble. Our generic local evolutionary strategy can be used to solve a wide range of synchronization and control problems.