Sustained Spatial Patterns of Activity in Neuronal Populations without Recurrent Excitation

Spatial patterns of neuronal activity arise in a variety of experimental studies. Previous theoretical work has demonstrated that a synaptic architecture featuring recurrent excitation and long-range inhibition can support sustained, spatially patterned solutions in integrodifferential equation models for activity in neuronal populations. However, this architecture is absent in some areas of the brain where persistent activity patterns are observed. Here we show that sustained, spatially localized activity patterns, or bumps, can exist and be linearly stable in neuronal population models without recurrent excitation. These models support at most one bump for each background input level, in contrast to the pairs of bumps found with recurrent excitation. We explore the shape of this bump as well as the mechanisms by which this bump is born and destroyed as background input level changes. Further, we introduce spatial inhomogeneity in coupling and show that this induces bump pinning: for a given starting position, bumps can exist only for a small, discrete set of background input levels, each with a unique corresponding bump width.