The role of network structure and time delays in shaping synchrony patterns in brain network models

Synchrony is a significant aspect of neuronal network dynamics, whereby oscillatory brain networks collectively coordinate to achieve various functions. Moreover, a plethora of experimental evidence exists suggesting a close correlation between abnormalities in neuronal synchronisation and various cognitive disorders. Thus, comprehending the mechanisms that underlie neural synchrony is crucial for gaining insight into fundamental brain processes, both in healthy and diseased states. Key factors influencing neural synchrony include the topological and dynamical properties of the network, and whilst significant progress has been made in recent years, our understanding of the role of network connectivity in the presence of time delays is incomplete. Here we explore the role of time delays on brain network dynamics by performing a bifurcation analysis on a ring of delay-coupled Wilson-Cowan masses. Our results indicate that ring network structures can promote a range of dynamics (including global synchrony, approximate anti-phase synchronisation, and chaos-like solutions) in a manner that depends upon the balance between coupling strength and delay time. We observe that emergent oscillations are generally either synchronous or anti-synchronous, and show that the transition between these various solutions is caused by either a torus or period doubling bifurcation of a stable periodic orbit. These regions are delineated by weakly chaotic borders that emerge as a result of the breakdown of the aforementioned torus. Moreover, as the time delay values further increase, the bifurcation diagrams exhibit a progressively more overlapped branching structure, which leads the system to exhibit more complex, metastable dynamics.