Localized activations in a simple neural field model

  • Herrmann J
  • Schrobsdorff H
  • Geisel T
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Abstract

A quarter of a century ago Amari (Biol. Cybernet. 27 (1977) 77-87) has presented a comprehensive and very elegant solution of the one-dimensional neural field equation. In the two-dimensional case analytical results on localized solutions are available under the assumption of rotational invariance, as numerical evidence indicates that no other stable solutions exist. We present analytic results for a special case of a "tophat" interaction function, which partially justifies the implicit assumption of circular solutions and allows us to discuss the possibility of non-generic deviations from circularity. © 2004 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Amari model
  • Bubbles
  • Circularity
  • Local excitation
  • Neural fields

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Authors

  • J. Michael Herrmann

  • Hecke Schrobsdorff

  • Theo Geisel

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