  We analyze a multilayer neural field model of spatial working memory,
focusing on the impact of interlaminar connectivity, spatial heterogeneity, and
velocity inputs. Models of spatial working memory typically employ networks
that generate persistent activity via a combination of local excitation and
lateral inhibition. Our model is comprised of a multilayer set of equations
that describes connectivity between neurons in the same and different layers
using an integral term. The kernel of this integral term then captures the
impact of different interlaminar connection strengths, spatial heterogeneity,
and velocity input. We begin our analysis by focusing on how interlaminar
connectivity shapes the form and stability of (persistent) bump attractor
solutions to the model. Subsequently, we derive a low-dimensional approximation
that describes how spatial heterogeneity, velocity input, and noise combine to
determine the position of bump solutions. The main impact of spatial
heterogeneity is to break the translation symmetry of the network, so bumps
prefer to reside at one of a finite number of local attractors in the domain.
With the reduced model in hand, we can then approximate the dynamics of the
bump position using a continuous time Markov chain model that describes bump
motion between local attractors. While heterogeneity reduces the effective
diffusion of the bumps, it also disrupts the processing of velocity inputs by
slowing the velocity-induced propagation of bumps. However, we demonstrate that
noise can play a constructive role by promoting bump motion transitions,
restoring a mean bump velocity that is close to the input velocity.
