Enhancing complex-network synchronization

Abstract. – Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in weighted networks with asymmetric coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically enhanced and may become positively correlated with heterogeneity, while the overall cost involved in the network coupling is significantly reduced as compared to the case of unweighted coupling. Networks of dynamical elements serve as natural models for a variety of systems, with examples ranging from cell biology to epidemiology to the Internet [1]. Many of these complex networks display common structural features, such as the small-world [2] and scale-free properties [3]. Small-world networks (SWNs) exhibit short average distance between nodes and high clustering [2], while scale-free networks (SFNs) are characterized by an algebraic, highly heterogeneous distribution of degrees (number of links per node) [3]. The interplay between