Effects of distributed transmission speeds on propagating activity in neural populations

Motivated by experimental evidence, a distribution of axonal transmission speeds is introduced into a standard field model of neural populations. The resulting field dynamics is analytically studied by a systematic investigation of the stability and bifurcations of equilibrium solutions. Using a perturbation approach, the effect of distributed speeds on bifurcations of equilibria are determined for general connectivity and speed distributions. In addition, a nonlinear analysis of traveling fronts is given. It is shown that the variance of the speed distribution affects the frequency of bifurcating periodic solutions and the phase speed of traveling waves. Moreover, a new effect is discovered where the introduction of axonal speed distributions leads to the maximization of the traveling front speed.