The broad edge of synchronization: Griffiths effects and collective phenomena in brain networks

Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronization running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchicalmodular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronization, halfway in the synchronous asynchronous spectrum. These states are best described as broad Griffithslike phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronization and stress the relevance of hybrid-Type transitions to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality. This article is part of the theme issue Emergent phenomena in complex physical and socio-Technical systems: from cells to societies .2022 The Author(s) Published by the Royal Society. All rights reserved.