Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 21: Neural Networks

DY 21.1: Talk

Tuesday, March 9, 2004, 10:15–10:30, H3

Localized solutions in neural fields — •Hecke Schrobsdorff, Michael Herrmann, and Theo Geisel — MPI für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstr. 10, D-37073 Göttingen

Neural fields provide a macroscopic description of the dynamics of activations in a layer of neurons. For one-dimensional layers the neural field equation has been solved virtually completely in an elegant way^[1]. For the two-dimensional problem most work has been devoted to spatially extended solutions. While being the point of main interest in [1], localized solutions have been treated analytically only for the trivial case of concentric configurations subject to circular perturbations^[2]. Although we can provide numerical evidence for the stable solutions being indeed concentric, a general analytical proof of this fact seems very difficult. In this contribution we simplify the model by the assumption of a specific form of the interactions. The model shows circular stable solutions and unstable solution of more complex shapes. Further we discuss applications of neural fields in neurobiology and robotics.

^[1] Amari S (1977) Biol Cybern 27.77-87.

^[2] Taylor J (1999) Biol Cybern 80, 393-409.