Hamburg 2001 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 42: Neuronale Netze / Statistische Physik fernab vom thermischen Gleichgewicht

DY 42.2: Vortrag

Donnerstag, 29. März 2001, 11:00–11:15, S 6

Unstable attractors in neural networks — •M. Timme, F. Wolf, and T. Geisel — MPI für Strömungsforschung, 37073 Göttingen

When analyzing models of neural networks in the brain, the attractor concept is highly important. As in all dissipative systems, attractors and their basin structure determine the system’s dynamics. Intuitively, attractors are thought of as stable invariant sets. However, invariant sets may also exist, which are attracting but simultaneously unstable, called unstable attractors. Such attractors appear to be exceptional cases that have to be constructed by tuning a parameter to a certain bifurcation value. Until now, they have only been found in physical systems for which the attractor in question is chaotic. Here we report a first example of a dynamical system, a neural network model, in which unstable periodic attractors arise naturally. These attractors are surrounded by basins of other attractors, whereas the full measure of their own basin is separated from the attractor. Unstable attractors prove typical for large networks and a wide range of parameters. Under the influence of noise these attractors create qualitatively new phenomena like attractor switching and attractor selection.