  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.
