Persistent fluctuations of activity in undriven continuum neural field models with power-law connections

We study the effect of random inhomogeneous connections on a continuous field description of neural tissue. We focus on a regime in which persistent random fluctuations in activity arise spontaneously in the absence of either time-varying or spatially inhomogeneous input. While present in real tissue and network models of discrete neurons, such behavior has not been reported in continuum models of this type. The activity contains frequencies similar to those seen experimentally. We consider a power-law envelope r(-alpha) for the inhomogeneity and present evidence that the statistical coherence (a measure of two-point correlation) rapidly percolates across the system as alpha is reduced below alphac approximately 1,2 in one and two dimensions, respectively.