Hierarchical transitions in multiplex adaptive networks of oscillatory units.

In this work, we consider two-layer multiplex networks of coupled Stuart-Landau oscillators. The first layer contains oscillators with amplitude heterogeneity and all-to-all adaptive links, while the second layer contains identical oscillators all-to-all coupled by links with constant weights. The links between different layers are adaptive and organized in a one-to-one manner. We study the evolution of one-layer and two-layer networks depending on intra- and interlayer coupling strengths and show hierarchical transitions between oscillatory and quenched regimes.