Mechanisms for activity spread in a neural field model

Field models of continuous neural networks incorporate nonlocal connectivities as well as finite axonal propagation velocities and lead therefore to delayed integral equations. For special choices of the synaptic footprint it is possible to reduce the integral model to a system of partial differential equations. One example is that of the inhomogeneous damped wave equation in one space dimension derived by Jirsa and Haken for exponential synaptic footprint. We show that this equation can be put into the form of a conservation law with nonlinear source, and explore numerically this representation. We find two mechanisms for the spread of the activity from an initially excited region.