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Significant research has investigated synchronisation in brain networks, but the bulk of this work has explored the contribution of brain networks at the macroscale. Here we explore the effects of changing network topology on functional dynamics in spatially constrained random networks representing mesoscale neocortex. We use the Kuramoto model to simulate network dynamics and explore synchronisation and critical dynamics of the system as a function of topology in randomly generated networks with a distance-related wiring probability and no preferential attachment term. We show networks which predominantly make short-distance connections smooth out the critical coupling point and show much greater metastability, resulting in a wider range of coupling strengths demonstrating critical dynamics and metastability. We show the emergence of cluster synchronisation in these geometrically-constrained networks with functional organisation occurring along structural connections that minimise the participation coefficient of the cluster. We show that these cohorts of internally synchronised nodes also behave en masse as weakly coupled nodes and show intra-cluster desynchronisation and resynchronisation events related to inter-cluster interaction. While cluster synchronisation appears crucial to healthy brain function, it may also be pathological if it leads to unbreakable local synchronisation which may happen at extreme topologies, with implications for epilepsy research, wider brain function and other domains such as social networks.
Mackay et al. (Tue,) studied this question.