title: Stability of localized patterns in neural fields.
abstract: We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case was treated comprehensively by Amari 30 years ago, two-dimensional neural fields are much less understood. We derive conditions for the stability for the main classes of localized solutions of the neural field equation and study their behavior beyond parameter-controlled destabilization. We show that a slight modification of the original model yields an equation whose stationary states are guaranteed to satisfy the original problem and numerically demonstrate that it admits localized noncircular solutions. Typically, however, only periodic spatial tessellations emerge on destabilization of rotationally invariant solutions.
authors.affiliation: Princeton University, Department of Molecular Biology, Lewis Thomas Lab 343A, Princeton, NJ 08544, U.S.A. kdoubrov@princeton.edu
authors.forename: Konstantin
authors.initials: K
authors.lastname: Doubrovinski
authors.forename: J Michael
authors.initials: JM
authors.lastname: Herrmann
mesh_terms: D000818:Animals; D002540:Cerebral Cortex / Q000166:cytology / Q000502:physiology*; D003491:Cybernetics; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D012371:Robotics