Neural field dynamics on a spherical cortical surface with long-range connectivity and finite propagation speed

The neuronal ensembles in cortical tissue, which tend to behave as single functional units, communicate
with each other and process information over time. Neural activity fields, in form of spatially continuous
networks, can be used to model a variety of neurobiological phenomena. The connection topology of
brain tissue is such that a cortical area is not only connected to its neighbors locally, but also has global
projection to distant areas via a fiber system. Such projections not only serve to organize local dynamics
within cortical areas but timing of these processes at different sites will affect the overall emerging pattern
and contributes to the macroscopic organization and global dynamics of neural activity. The dynamics
of this neural field activity gives rise to pattern formation phenomena and self-organization. Our
macroscopic spatiotemporal pattern formation approach assumes the existence of an order parameter
dynamics and leads to phenomenological models to understand the collective phenomena even though
the microscopic dynamics is not completely known. We are investigating how the emerging patterns
depend on the space-time structure of the coupling between functional units i.e. long-range
heterogeneous pathways coupling strength (space) and the axonal time delay due to propagation with
finite speed between areas (time). We analyze the stability of the rest-state activity of a neural field as
manipulating heterogeneous two-point connections varies network connection topology in two geometries with periodic boundary conditions: a closed one-dimensional loop and a closed spherical 2-
D cortical surface.