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

In: Neural Fields

Author

Listed:
  • Axel Hutt

    (Neurosys, Inria CR Grand Est – Nancy)

  • Nicolas Rougier

    (Mnemosyne, Inria Bordeaux Sud-Ouest
    Bordeaux University, LaBRI, UMR 5800 CNRS
    Institute of Neurodegenerative Diseases, UMR 5293)

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.

Suggested Citation

  • Axel Hutt & Nicolas Rougier, 2014. "Numerical Simulation Scheme of One- and Two Dimensional Neural Fields Involving Space-Dependent Delays," Springer Books, in: Stephen Coombes & Peter beim Graben & Roland Potthast & James Wright (ed.), Neural Fields, edition 127, chapter 0, pages 175-185, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54593-1_6
    DOI: 10.1007/978-3-642-54593-1_6
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