Spike-to-Field Mechanisms of Turbulence-Like Dynamics in Spatial Spiking Neural Networks

Zequan Liu

Neural avalanches and turbulence-like brain dynamics are usually measured after neural activity has been coarse-grained into continuous fields, leaving open which spike-level mechanisms can generate these macroscopic observables. We build a spatial leaky integrate-and-fire spiking neural network and explicitly transform spikes into activity-density and Hilbert phase fields. A delayed, distance-dependent, passive-dendrite regime reproducibly generates turbulence-like field structure, including high-amplitude phase-defect tracks, structure-function scaling, and power-law-favored continuous-field avalanche tails. Controls show that firing rate, vortex count, and avalanche tail fits are individually insufficient: destroying delayed propagation, dendritic filtering, or spike timing suppresses key field signatures, while random-space nulls can retain many mathematical phase defects but show weaker spatial structure and synaptic-delay transfer. Biologically motivated gates further shape the regime: PV-like perisomatic inhibition clamps phase dynamics, SST-like dendritic inhibition and projection-specific inhibitory facilitation preserve long-lived tracks, and a rate-constrained…