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.