Evolution equations for neural networks with arbitrary spatial structure

The question of how to describe networks in which the range of connections is restricted or in which the connection density is not uniform in space is still unanswered. The purpose of the paper is to remedy this situation for the case where the range of the connections is large compared to the average distance between neighbouring neurons. The number of connections to and from each neuron are assumed to be large as well. The microscopic master equation is used to derive a partial differential equation for the position- and time-dependent correlations between the system state and the stored patterns. The equation can be used to study networks with finite range connections (not necessarily symmetric), the behaviour of domain boundaries and information transport