Traveling fronts and wave propagation failure in an inhomogeneous neural network

We use averaging and homogenization theory to study the propagation of traveling wavefronts in an inhomogeneous excitable neural medium. Motivated by the functional architecture of primary visual cortex, we model the inhomogeneity as a periodic modulation in the long-range neuronal connections. We derive an expression for the effective wavespeed and show that propagation failure can occur if the speed is too slow or the degree of inhomogeneity is too large. We find that there are major qualitative differences in the wavespeed for different choices of the homogenized weight distribution.