Neural field dynamics with local and global connectivity and time delay

Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in particular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, we investigate the stability of the rest-state activity of a neural field as a function of its connectivity. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix, as well as by variation of connectivity strength and a finite transmission speed. The latter results in a time delay of communication among individual brain areas. We demonstrate that the local connectivity generates the well-known power-law behaviour of the electroencephalographic power spectrum with an exponent close to -2, whereas the global connections generate a more characteristic line spectrum. These spectral characteristics are routinely observed in large-scale topographies of the human brain.