Coupling layers regularizes wave propagation in laminar stochastic neural fields

Abstract: We study the effects of coupling between layers of stochastic neural field models with laminar structure. In particular, we focus on how the propagation of waves of neural activity in each layer is affected by the coupling. Synaptic connectivities within and between each layer are determined by integral kernels of an integrodifferential equation describing the temporal evolution of neural activity. Excitatory neural fields, with purely positive connectivities, support traveling fronts in each layer, whose speeds are increased when coupling between layers is considered. Studying the effects of noise, we find coupling also serves to reduce the variance in the position of traveling fronts, as long as the noise sources to each layer are not completely correlated. Neural fields with asymmetric connectivity support traveling pulses whose speeds are decreased by interlaminar coupling. Again, coupling reduces the variance in traveling pulse position, when noise is considered that is not totally correlated between layers. To derive our stochastic results, we employ a small-noise expansion, also assuming interlaminar connectivity scales similarly. Our asymptotic results agree reasonably with accompanying numerical simulations.