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.
Mayer
N Michael
NM
JST ERATO Asada Project, FRC-I, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka, Japan. michael@jeap.org
Browne
Matthew
M
Herrmann
J Michael
JM
Asada
Minoru
M
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