Localized activations in a simple neural field model

J. Michael Herrmann, Hecke Schrobsdorff, Theo Geisel

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)679 - 684
Number of pages6
JournalNeurocomputing
Volume65–66
DOIs
Publication statusPublished - 2005

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