Periodic Traveling Waves in a One-Dimensional Integrate-and-Fire Neural Network

We study the existence of one-dimensional periodic traveling waves in a network of coupled integrate-and-fire neurons. We consider two special cases for the kernel of the coupling function, namely finite support and exponential decay. In these cases, we analytically derive a self-consistency equation that generates an explicit dispersion relation between velocity of the traveling waves and their corresponding wavelength. Simulations show how initiation of activity in one part of a network can cause each cell in the network to fire a succession of spikes, with interspike intervals converging toward the spiking period for the periodic regime