Network structure and time delays shape synchronization patterns in brain network models

In this paper, we investigate synchronization patterns and coherence for a network of delayed Wilson-Cowan nodes. To capture information processing across different brain regions, our model incorporates two distinct delays: an intra-nodal delay that reflects the time signals take to travel within a cortical region due to local circuitry and an inter-nodal delay representing the longer communication times associated with white matter connections between brain areas. To investigate the role of network topology, we consider a range of toy network structures as well as the known (macro-scale) cortical structure of the Macaque monkey. We examine how global network dynamics are shaped by a combination of network configuration, coupling strength, and time delays. Our focus lies on two dynamic measures: synchrony and metastability, the latter reflecting the temporal variation of the former, both crucial for the brain's real-time functionality. Our investigation identifies extensive regions within the system's parameter space where the synchronized state exhibits transverse instabilities. These instabilities give rise to diverse dynamical behaviors contingent upon the network architecture and the interplay between coupling strength and time delay. While similar complex partially synchronized states existed for all network topologies considered, the cortical network demonstrated time-dependent behaviors, such as phase cluster dynamics, which were absent in the toy network architectures, and which are considered crucial in its ability to orchestrate complex information processing and behavior. Additionally, we illustrate how delays can regulate a cortical network with chaotic local dynamics, thus emphasizing the potential importance of delays in suppressing pathological spreading dynamics.