Traveling waves in a one-dimensional integrate-and-#re neural network with #nite support connectivity

We study the existence of traveling waves in a one-dimensional network of integrate-and-#re neurons with #nite support coupling. We show that when the reset after spiking is su2ciently low, the interspike intervals (ISIs) for a traveling wave with an explicit #rst wave front can be computed. Further, we analytically derive a self-consistency equation that generates an explicit dispersion relation between the velocity of periodic traveling waves and their corresponding ISIs. Finally, we prove that the ISIs of non-periodic traveling waves converge to the ISI of the periodic waves with the same speed. c © 2002 Elsevier Science B.V. All rights reserved.