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Abstract

We analyze how the structure of complex networks of non-identical oscillators influences synchronization in the context of the Kuramoto model. The complex network metrics assortativity and clustering coefficient are used in order to generate network topologies of Erdös–Rényi, Watts–Strogatz, and Barabási–Albert types that present high, intermediate, and low values of these metrics. We also employ the total dissonance metric for neighborhood similarity, which generalizes to networks the standard concept of dissonance between two non-identical coupled oscillators. Based on this quantifier and using an optimization algorithm, we generate Similar, Dissimilar, and Neutral natural frequency patterns, which correspond to small, large, and intermediate values of total dissonance, respectively. The emergency of synchronization is numerically studied by considering these three types of dissonance patterns along with the network topologies generated by high, intermediate, and low values of the metrics assortativity and clustering coefficient. We find that, in general, low values of these metrics appear to favor phase locking, especially for the Similar dissonance pattern. The topology of networks of phase oscillators plays a very important role on the synchronization of the system. The individual dynamics of each oscillator, characterized by their individual frequencies, also play a very important role, which is not completely understood. What effect the emergency of cycles, the connection of nodes with close or very distinct degree have on synchronization? Furthermore, is this affected by the natural frequencies of the oscillators being connected? These questions are also important if we take into consideration the emergence of synchronization phenomena in nature that leads the involved agents from the disorder to order in a scenario in which the agent interconnections are not all-to-all. Here, we investigate these issues.