Enhancing Synchronization in Systems of Non-identical Kuramoto Oscillators

In this paper we present a summary of some of our recent results on the synchronization of non-identical Kuramoto oscillators coupled via complex networks. Crucially, we emphasize that the systems overall degree of synchronization cannot only be improved by tuning properties of the coupling network, but also by a correlated assignment of oscillators to nodes. In the context of symmetrical coupling via undirected networks we discuss network characteristics and correlations between the oscillator placement on the nodes of the network that enhance the overall degree of synchronization. Several simple rules to improve the degree of synchronization in a system are given, such as, e.g. (i) anti-correlated placement of adjacent oscillators, and (ii) placement of oscillators with native frequencies far off the mean in the centre of the network and (iii) placement of oscillators with native frequencies close to the mean at the periphery of the network. The influence of oscillator correlations on synchronization transition is discussed as well. Finally, we analyze the question whether a a globally synchronized system can be generated by rewirings that improve the local synchronizability.