Numerical simulation scheme of one- and two dimensional neural fields involving space-dependent delays

Abstract

Neural Fields describe the spatiotemporal dynamics of neural populations involving spatial axonal connections between neurons. These neuronal connections are delayed due to the finite axonal transmission speeds along the fibers inducing a distance-dependent delay between two spatial locations. The numerical simulation in 1-dimensional neural fields is numerically demanding but may be performed in a reasonable run time by implementing standard numerical techniques. However 2-dimensional neural fields demand a more sophisticated numerical technique to simulate solutions in a reasonable time. The work presented shows a recently developed numerical iteration scheme that allows to speed up standard implementations by a factor 10-20. Applications to some pattern forming systems illustrate the power of the technique.