Metaplex Networks: Influence of the Exo-Endo Structure of Complex Systems on Diffusion

Complex networks represent the global behavior of complex systems in terms of interacting subcomponents. This article introduces metaplex networks, which include the internal structure, dynamics and function of these subcomponents, and analyzes their interplay with the network structure for the global dynamics of the system. We illustrate the use of this framework for diffusion and superdiffusion in metaplexes whose nodes are domains in $\mathbb{R}^n$. Long-range hopping leads to superdiffusive behaviour across the whole metaplex, and it survives independently of the internal structure. The global diffusion dynamics, however, strongly reflects the geometry of the nodes, the nature of the coupling, as well as the internal diffusion processes. We provide analytical and numerical results to shed light on this interaction of internal and external dynamics.