Synchronization of heterogeneous oscillators under network modifications: perturbation and optimization of the synchrony alignment function (Q2827058)

This paper concerns the synchrony alignment function (SAF) which quantifies the relationship between phase oscillators' frequencies and the structure of the network formed by coupling them, in the sense of providing an objective measure for the network's ability to synchronize. The main results involve analysing the effect on the SAF of adding or removing edges from the network. This allows the authors to rank both the existing edges and potential new edges in terms of the effect of their removal or addition on the value of the SAF, and thus the synchronizability of the network. The authors also develop gradient-descent algorithms for the optimisation of synchrony, in which the network can be rewired in several different ways (only removing edges, only adding edges, rewiring a fixed number of edges). They also demonstrate the success of their algorithms in less than ideal circumstances. The results are all well-illustrated with numerical examples.