Symmetries, non-Euclidean metrics, and patterns in a Swift–Hohenberg model of the visual cortex

N. Michael Mayer, Matthew Browne, Michael Herrmann, Minoru Asada

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this work is to investigate the effect of the shift-twist symmetry on pattern formation processes in the visual cortex. First, we describe a generic set of Riemannian metrics of the feature space of orientation preference that obeys properties of the shift-twist, translation, and reflection symmetries. Second, these metrics are embedded in a modified Swift–Hohenberg model. As a result we get a pattern formation process that resembles the pattern formation process in the visual cortex. We focus on the final stable patterns that are regular and periodic. In a third step we analyze the influences on pattern formation using weakly nonlinear theory and mode analysis. We compare the results of the present approach with earlier models.
Original languageEnglish
Pages (from-to)63-78
Number of pages16
JournalBiological Cybernetics
Volume99
Issue number1
DOIs
Publication statusPublished - Jul 2008

Keywords

  • Orientation maps in visual cortex
  • Pattern formation process
  • Shift-twist symmetry

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