Berlin 2015 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 62: Poster - Dynamics

DY 62.4: Poster

Thursday, March 19, 2015, 16:00–18:00, Poster A

Slow points and adiabatic fixed points in small neural networks — •Hendrik Wernecke and Claudius Gros — Institut für Theoretische Physik, Goethe-Universität, Max-von-Laue-Str. 1, Frankfurt am Main, Germany

Fixed points and limit cycles play an important role for the dynamics of neural networks. However, in the present work we examine the influence of slow points on the flow and motion in phase space.

A special kind of slow points, so-called attractor remnants, come into existence when adding a slowly varying dimension to a (faster) system. At the fixed points of the faster system the flow does no longer necessarily vanish, but these points are still present in the network as slow points. In order to examine the influence of the slow points on the compound system, the concept of adiabatic fixed points is introduced and the effect on small neural networks is discussed.

It turns out that with the help of these remnants one can describe a mechanism that spans limit cycles and determines the dynamical behaviour of the system. To analyze and compare systems of different dimensionality measures such as the system*s speed in phase space or the distance of the trajectory to the adiabatic fixed points are defined and their properties are examined.