Localized activity patterns in excitatory neuronal networks.

The existence of localized activity patterns, or bumps, has been investigated in a variety of spatially distributed neuronal network models that contain both excitatory and inhibitory coupling between cells. Here we show that a neuronal network with purely excitatory synaptic coupling can exhibit localized activity. Bump formation ensues from an initial transient synchrony of a localized group of cells, followed by the emergence of desynchronized activity within the group. Transient synchrony is shown to promote recruitment of cells into the bump, while desynchrony is shown to be good for curtailing recruitment and sustaining oscillations of those cells already within the bump. These arguments are based on the geometric structure of the phase space in which solutions of the model equations evolve. We explain why bump formation and bump size are very sensitive to initial conditions and changes in parameters in this type of purely excitatory network, and we examine how short-term synaptic depression influences the characteristics of bump formation.