# Metaplex networks: influence of the exo-endo structure of complex systems on diffusion

## TL;DR

This paper introduces the concept of metaplexes, analyzing how internal node structures and their interconnections influence diffusion processes, with applications to landscape and brain systems.

## Contribution

It defines the metaplex framework and investigates how internal structures and coupling parameters affect global dynamics in complex systems.

## Key findings

- Internal node structure can dominate global dynamics in brain metaplexes.
- Node internal coupling location influences diffusion behavior.
- Internal structure plays a regulatory role in landscape metaplexes.

## Abstract

In a complex system the interplay between the internal structure of its entities and their interconnection may play a fundamental role in the global functioning of the system. Here, we define the concept of metaplex, which describes such trade-off between internal structure of entities and their interconnections. We then define a dynamical system on a metaplex and study diffusive processes on them. We provide analytical and computational evidences about the role played by the size of the nodes, the location of the internal coupling areas, and the strength and range of the coupling between the nodes on the global dynamics of metaplexes. Finally, we extend our analysis to two real-world metaplexes: a landscape and a brain metaplex. We corroborate that the internal structure of the nodes in a metaplex may dominate the global dynamics (brain metaplex) or play a regulatory role (landscape metaplex) to the influence of the interconnection between nodes.