Numerical Simulation Scheme of One- and Two Dimensional Neural Fields Involving Space-Dependent Delays

Axel Hutt () and Nicolas Rougier
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Axel Hutt: Neurosys, Inria CR Grand Est – Nancy
Nicolas Rougier: Mnemosyne, Inria Bordeaux Sud-Ouest

Chapter Chapter 6 in Neural Fields, 2014, pp 175-185 from Springer

Abstract: 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.

Keywords: Transmission Delay; Transmission Speed; Neural Field; Neural Field Model; Ring Ring (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54593-1_6

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DOI: 10.1007/978-3-642-54593-1_6

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