Optimization of synchronizability in multiplex networks by rewiring one layer

摘要

The mathematical framework of multiplex networks has been increasingly realized as a more suitableframework for modeling real-world complex systems. In this work, we investigate the optimization ofsynchronizability in multiplex networks by evolving only one layer while keeping other layers fixed. Ourmain finding is to show the conditions under which the efficiency of convergence to the most optimal structure isalmost as good as the case where both layers are rewired during an optimization process. In particular, interlayercoupling strength responsible for the integration between the layers turns out to be a crucial factor governing theefficiency of optimization even for the cases when the layer going through the evolution has nodes interactingmuch more weakly than those in the fixed layer. Additionally, we investigate the dependency of synchronizabilityon the rewiring probability which governs the network structure from a regular lattice to the random networks.The efficiency of the optimization process preceding evolution driven by the optimization process is maximumwhen the fixed layer has regular architecture, whereas the optimized network is more synchronizable for the fixedlayer having the rewiring probability lying between the small-world transition and the random structure.