Pattern phase diagram of spiking neurons on spatial networks.

Abstract

We study an abstracted model of neuronal activity via numerical simulation and report spatiotemporal pattern formation and criticallike dynamics. A population of pulse coupled, discretized, relaxation oscillators is simulated over networks with varying edge density and spatial embeddedness. For intermediate edge density and sufficiently strong spatial embeddedness, we observe a spatiotemporal pattern in the field of oscillator phases, visually resembling the surface of a frothing liquid. Increasing the edge density results in a distribution of neuronal avalanche sizes which follows a power law with exponent one (Zipf's law). Further increasing edge density yields metastability between pattern formation and synchronization, before transitioning entirely into synchrony.