Synaptically generated wave propagation in excitable neural media

We study the propagation of solitary waves in a one-dimensional network of excitable integrate-and-fire neurons with axo-dendritic synaptic coupling. We show that for small axonal delays there exists a stable solitary wave, and derive a power scaling law for the velocity as a function of the coupling. In the case of large axonal delays and fast synapses we establish that the solitary wave can destabilize via a Hopf bifurcation in the firing times.