Symmetries, non-Euclidean metrics, and patterns in a Swift-Hohenberg model of the visual cortex.
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.
JST ERATO Asada Project, FRC-I, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka, Japan. michael@jeap.org
N Michael
NM
Mayer
Matthew
M
Browne
J Michael
JM
Herrmann
Minoru
M
Asada
D000200:Action Potentials / Q000502:physiology; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D016011:Normal Distribution; D009949:Orientation / Q000502:physiology*; D010364:Pattern Recognition, Visual / Q000502:physiology*; D014793:Visual Cortex / Q000502:physiology*; D014794:Visual Fields / Q000502:physiology