Inter-layer competition in adaptive multiplex network

We consider competition between layers in adaptive multiplex networks of phase oscillators, where adaptation principles (which cause intra-layer topology evolution) are inspired by real world homophily and homeostasis phenomena. Our model yields the emergence of both scale-free topologies and meso-scale structures in the layers, for an appropriate choice of the control parameters. We further report that the growth of the number of interacting layers leads to a decrease of the global order, due to inter-layer structural competition. However, the increase of the system's scale can effect local synchronization between neighboring (or strongly coupled) nodes. Such unforeseen phenomena is connected with the nature of the competitive mechanism, which implies the rivalry for optimal structure within the whole system, a situation occurring in a variety of natural systems.