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

Axel Hutt 1 Nicolas P. Rougier 2, 3
1 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
2 Mnemosyne - Mnemonic Synergy
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest, IMN - Institut des Maladies Neurodégénératives [Bordeaux]
Abstract : Neural Fields describe the spatio-temporal 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.
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Axel Hutt, Nicolas P. Rougier. Numerical simulation scheme of one-and two-dimensional neural fields involving space-dependent delays. P. Beim Graben and S. Coombes and R. Potthast and J.J. Wright. Neural Field Theory, Springer, 2014. ⟨hal-00872132⟩

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