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arXiv · 1408.2194

Assortative mixing enhances the irreversible nature of explosive synchronization in growing scale-free networks

I. Sendiña-Nadal·I. Leyva·A. Navas·J. A. Villacorta-Atienza·J. A. Almendral·Z. Wang·S. Boccaletti
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Abstract

We discuss the behavior of large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and network's degrees. In particular, we show that the further presence of degree-degree correlation in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network's state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in growing scale-free networks. This latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization.

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I. Sendiña-Nadal, I. Leyva, A. Navas, J. A. Villacorta-Atienza, J. A. Almendral, Z. Wang, S. Boccaletti. 2014-08-10. Assortative mixing enhances the irreversible nature of explosive synchronization in growing scale-free networks. https://doi.org/10.1103/physreve.91.032811

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