In this talk I will introduce the concept of metaplexes and the dynamical systems on them. A metaplex combines the internal structure of the entities of a complex system with the discrete interconnectivity of these entities in a global topology. We focus here on the study of diffusive processes on metaplexes, both model and real-world examples. We provide theoretical and computational evidence pointing out the role of the endo- and exo-structure of the metaplexes in their global dynamics, including the role played by the size of the nodes, the location of sinks and sources, and the strength and range of the coupling between nodes. We show that the internal structure of brain regions (corresponding to the nodes of the network) in the macaque visual cortex metaplex dominates almost completely the global dynamics. On the other hand, in the linear metaplex chain and the landscape metaplex the diffusion dynamics display a combination of the endo- and exo-dynamics, which we explain analytically and in numerical results. Metaplexes are expected to facilitate the understanding of complex systems in an integrative way, which combine dynamical processes inside the nodes and between them.
Presential in the IFISC seminar room, Zoom stream at
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