Unique superdiffusion induced by directionality in multiplex networks

Abstract The multilayer network framework has served to describe and uncover a number of novel unforeseen physical behaviors regimes in interacting complex systems. However, the majority existing studies are built on undirected networks while most systems nature exhibit directed interactions. Here, we propose analyze diffusive dynamics consisting at least one layer. We rigorously demonstrate that directionality can fundamentally change behavior dynamics: from monotonic (in systems) non-monotonic diffusion with respect interlayer coupling strength. Moreover, for certain configurations, induce unique superdiffusion regime intermediate values coupling, wherein is even faster than corresponding theoretical limit systems, i.e. integrated obtained aggregation each theoretically numerically show existence fully determined by layer topological overlap between layers. further provide formulation displaying superdiffusion. Our results highlight significance incorporating multilevel networked dynamical processes interconnected directionality.