Optimally frequency-synchronized networks of nonidentical Kuramoto oscillators.

ABSTRACT

Based on a local greedy numerical algorithm, we compute the topology of weighted, directed, and unlimited extension networks of nonidentical Kuramoto oscillators which simultaneously satisfy two criteria (i) global frequency synchronization and (ii) minimum total mass of the connection weights. This problem has been the subject of many previous interesting studies; in the present paper, no a priori constraint is imposed, either on the form or on the dynamics of the connections. The results are surprising the optimal networks turn out to be strongly symmetric, to be very economical, and to display a strong rich club structure, and in addition to the already reported strong correlation between natural frequencies and the weight of incoming connections we also observe a correlation, even more marked, between these same natural frequencies and the weight of outgoing connections. The latter result is at odds with theoretical predictions.