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

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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Cited by in corpus (10)

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• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Explosive Phenomena in Complex Networks
• Effect of assortative mixing in the second-order Kuramoto model
• Reduction of oscillator dynamics on complex networks to dynamics on complete graphs through virtual frequencies
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• Opportunities and challenges in partitioning the graph measure space of real-world networks
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