Wave fronts in inhomogeneous neural field models

In this work we investigate the influence of inhomogeneities on wave front propagation in an excitatory neural field model describing synaptic activity in the absence of delays. This allows the derivation of the spatial (and hence temporal) behaviour of the front velocity under the assumption that the front is approximatively homogeneous in a very small time window. With this assumption we can also derive the spatiotemporal behaviour of the membrane potential analytically in the vicinity of the wave front. In addition to this we investigate stationary solutions such as standing wave fronts and localised activity (so-called bumps) to determine the existence condition of travelling and standing fronts. Numerical results are included to point out the accordance of theory and simulation.