Random fluctuations of the firing rate function in a continuum neural field model.

We incorporate a source of noise into a continuum neural field model by allowing the firing threshold to fluctuate noisily about a mean value, and examine traveling wave front solutions. Under certain conditions we are able to calculate the first and second moments of the distributions of the resulting time varying front speed and shape. This is then compared with more complete numerical solutions. Fluctuations in the wave front speed and in the shape (i.e., fluctuations in activity at particular coordinate positions across the wave front) were found to increase as the magnitude of the fluctuations in firing threshold increased. The mean speed was found to increase as the magnitude of the fluctuations increases. The role of the correlation time for the threshold variation is also investigated. We also study the role of threshold fluctuations in the failure of front propagation, both in the fast and slow varying noise limits.