Liapunov functional for a delayed integro-differential equation model of a neural field

摘要

We find a non-local energy functional for a scalar neural field with two stable steady states. The time evolution of the membrane potential of the network can be obtained from the gradient flow of this functional. It is shown that this approach can be used to energetically explain some of the properties of traveling wave fronts connecting the two stable states, such as the direction of the propagation velocity.