title: Stationary bumps in networks of spiking neurons.
abstract: We examine the existence and stability of spatially localized "bumps" of neuronal activity in a network of spiking neurons. Bumps have been proposed in mechanisms of visual orientation tuning, the rat head direction system, and working memory. We show that a bump solution can exist in a spiking network provided the neurons fire asynchronously within the bump. We consider a parameter regime where the bump solution is bistable with an all-off state and can be initiated with a transient excitatory stimulus. We show that the activity profile matches that of a corresponding population rate model. The bump in a spiking network can lose stability through partial synchronization to either a traveling wave or the all-off state. This can occur if the synaptic timescale is too fast through a dynamical effect or if a transient excitatory pulse is applied to the network. A bump can thus be activated and deactivated with excitatory inputs that may have physiological relevance.
authors: C R
authors: CR
authors: Laing
authors: C C
authors: CC
authors: Chow
mesh_terms: D000200:Action Potentials; D000818:Animals; D019416:Head Movements / Q000502:physiology; D008568:Memory / Q000502:physiology; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D051381:Rats; D009435:Synaptic Transmission / Q000502:physiology; D014795:Visual Pathways / Q000166:cytology / Q000502:physiology*