Title: Symmetries and synchronization in multilayer random networks,
Abstract: In the light of the recently proposed scenario of asymmetry-induced
synchronization (AISync), in which dynamical uniformity and consensus in a
distributed system would demand certain asymmetries in the underlying network,
we investigate here the influence of some regularities in the interlayer
connection patterns on the synchronization properties of multilayer random
networks. More specifically, by considering a Stuart-Landau model of complex
oscillators with random frequencies, we report for multilayer networks a
dynamical behavior that could be also classified as a manifestation of AISync.
We show, namely, that the presence of certain symmetries in the interlayer
connection pattern tends to diminish the synchronization capability of the
whole network or, in other words, asymmetries in the interlayer connections
would enhance synchronization in such structured networks. Our results might
help the understanding not only of the AISync mechanism itself, but also its
possible role in the determination of the interlayer connection pattern of
multilayer and other structured networks with optimal synchronization
properties.