Existence and Stability of Standing and Traveling Wave Solutions Arising from Synaptically Coupled Neuronal Networks

We consider three variations of neuronal network models and apply mathematical analysis to investigate standing and traveling wave solutions to the models. We consider solutions for both the scalar case and the system of equations. We establish existence and uniqueness of the solutions and determine the stability/instability of the solutions to the integral differential model equations. In addition we investigate the influence of sodium currents on the solutions. We perform a speed analysis to determine the effect of various biological parameters on the wave speed and wave structure.