Bifurcation of learning and structure formation in neuronal maps

¹ Department of Applied Mathematics and Computer Science, Technical University of Denmark 2800 Kongens Lyngby, Denmark
² Interdisciplinary Center for Scientific Computing, University of Heidelberg - 69120 Heidelberg, Germany
³ Physik Department & BCCN – Munich, Technische Universität München 85747 Garching bei München, Germany

Received: 23 May 2014
Accepted: 28 October 2014

Abstract

Most learning processes in neuronal networks happen on a much longer time scale than that of the underlying neuronal dynamics. It is therefore useful to analyze slowly varying macroscopic order parameters to explore a network's learning ability. We study the synaptic learning process giving rise to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance.