Synchrony in excitatory neural networks
Neural Computation
What matters in neuronal locking?
Neural Computation
Populations of spiking neurons
Pulsed neural networks
Rate models for conductance-based cortical neuronal networks
Neural Computation
Solitary Waves of Integrate-and-Fire Neural Fields
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
A Unified Approach to Building and Controlling Spiking Attractor Networks
Neural Computation
Stochastic dynamics of a finite-size spiking neural network
Neural Computation
Stability of localized patterns in neural fields
Neural Computation
Systematic fluctuation expansion for neural network activity equations
Neural Computation
Dynamics of feature categorization
Neural Computation
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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.