Abstract
We explore how layered architectures influence the dynamics of stochastic neural field models. Our main focus is how the propagation of waves of neural activity in each layer is affected by interlaminar 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 reduces 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. Asymptotic analysis is performed using a small-noise expansion, assuming interlaminar connectivity scales similarly.
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