title: Circular stationary solutions in two-dimensional neural fields.
abstract: Stationary solutions are studied in two-dimensional homogeneous neural fields of the lateral-inhibition type. It is shown that in extending the one-dimensional theory to two dimensions, new phenomena arise. We discuss the conditions for the existence of localized solutions analogous to the one-dimensional theory and show that they are no longer sufficient in two dimensions. We give indications for the existence of mono- and bistable dynamics as known from the one-dimensional theory and, additionally, a tri-stable type of dynamic in two-dimensional neural fields, where, depending on the input, excitation dies out, spreads without limit, or causes a stable localized excitation.
authors.affiliation: Institut für Informatik, Universität Leipzig, Germany. herrad@informatik.uni-leipzig.de
authors.forename: H
authors.initials: H
authors.lastname: Werner
authors.forename: T
authors.initials: T
authors.lastname: Richter
mesh_terms: D001921:Brain / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009433:Neural Inhibition / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D012677:Sensation / Q000502:physiology