Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Dienstag
DY 20.4 Di 10:30 H2
Interaction of filaments in an excitable chemical reaction —
•Ulrich Storb 1 , Camilo Rodriguez Neto 2 , Markus Bär 3 , and
Stefan C. Müller 1 — 1 Otto-von-Guericke-Universität, Institut für
Experimentelle Physik, Universitätsplatz 2, D-39106 Magdeburg — 2 Carl
von Ossietzky Universität, Institut für Chemie und Biologie des Meeres,
Carl-von-Ossietzky 9-11, D-26111 Oldenburg — 3 Max-Planck-Institute
für die Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden
Two-dimensional Belousov-Zhabotinsky reaction systems (BZRsystems)
are often dominated by spiral waves, i.e. a spiral shaped reaction
front spatially mediates a certain frequency behavior. In three
dimensions the variety of exhibited wave phenomena is much broader.
Organizing centers of these dynamical structures are phase singularities,
which in three dimensions take the shape of curves (filaments). Along a
filament the spatially distributed oscillations become synchronized. Temporally
and spatially resolved observations of chemical wave structures
are possible by optical tomography. We present results of a study on the
interaction of such vortex like wave structures, resp. their filaments. It
is known that the frequency of a spiral is effected by the presence of
a further phase singularity; the effect thereby depends on the distance
between the spiral cores. In three dimensions the distance between the
organizing centers is not unique, therefore there is a competition of various
frequency determining processes. The result is a complex interaction
which will be reported.
DY 20.5 Di 10:45 H2
Modeling of filament interactions in a three-dimensional excitable
reaction-diffusion system — •Markus Bär 1 , Camilo Rodriguez
Neto 1,2 , Ulrich Storb 3 , and Stefan C. Müller 3 — 1 Max-
Planck-Institute für die Physik komplexer Systeme, Nöthnitzer Strasse
38, D-01187 Dresden — 2 Carl von Ossietzky Universität, Institut für
Chemie und Biologie des Meeres, Carl-von-Ossietzky 9-11, D-26111 Oldenburg
— 3 Otto-von-Guericke-Universität, Institut für Experimentelle
Physik, Universitätsplatz 2, D-39106 Magdeburg
Motivated by recent experiments in a chemical reaction, we study the
interaction of scroll waves, the three dimensional extension of rotating
DY 21 Neural Networks
spirals. Such scroll waves in excitable media possess in any planar cut
through the volume a singularity around which the concentration profile
rotates. The line that connects these centers is known as a filament.
Here, we look at the interaction of corotating and counterrotating nonparallel
filaments in numerical simulations of a generic excitable media,
the Barkley model. In both cases, we observe repulsion and reconnection
of the filaments in the areas where they approach each other closest. The
interaction is accompanied by the generation of a local twisting and bending
of the filament. This effects are explained by a decrease of rotation
frequency around the filament due to local interactions. The bending is
crucial for the unusual reconnection of corotating filaments, which is usually
forbidden by topological arguments. We also discuss related effects
in two-dimensions and three-dimensional heterogeneous media.
DY 20.6 Di 11:00 H2
Detecting non-linearities in data sets. Characterization of
Fourier phase maps using the Weighting Scaling Indices. —
•Roberto Monetti, Wolfram Bunk, Ferdinand Jamitzky,
Christoph Raeth, and Gregor Morfill — CIPS, Max-Planck-Inst.
f. extraterr. Physik, Gaching
The analysis of the linear properties (LP) (power spectrum, etc) is the
first step in the characterization of data sets. However, given an image
for instance one can generate a new one by shuffling the Fourier phases.
The new image looks different though the phase shuffling process keeps
the LP. Then, the Fourier phases contain information beyond the LP
called non-linear properties (NLP). A challenging problem is the characterization
of the information contained in the Fourier phases. We present
a method to detect NLP in arbitrary data sets. With a set of Fourier
phases {φ� k } and a phase shift � ∆, we represent the phase information on
a 2D space via the phase maps M = {(φ� k , φ� k+ � ∆ )}. The information rendered
on this space is analyzed using the spectrum of weighting scaling
indices to detect phase coupling at any scale � ∆. We have applied our
method to the time series of the logarithmic stock returns of the Dow
Jones. Applications to higher dimensional data are straighforward. The
results indicate that the Dow Jones time series exhibits highly significant
signatures of a strong non-linear behavior.
Zeit: Dienstag 10:15–11:30 Raum: H3
DY 21.1 Di 10:15 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.
DY 21.2 Di 10:30 H3
Modelling Brain Function under Noise and Time-Delayed Feedback:
First Results — •Oliver Holzner and Eckehard Schöll
— Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse
36, D–10623 Berlin
Starting from an oscillator model of individual neurons, clusters and
meta-clusters of neurons (inhomogeneous, noisy, with transmission delay,
and asymmetric coupling) will be described, as well as the influence of
time-delayed internal and external feedback on electromagnetic observables.
This type of model is believed to be of clinical relevance, e.g. for
symptom blocking in case of Parkinson’s disease and/or epilepsy.
DY 21.3 Di 10:45 H3
Topological Speed Limits to Network Synchronization — •Marc
Timme, Fred Wolf, and Theo Geisel — Max-Planck-Institut für
Strömungsforschung, Bunsenstr. 10, 37073 Göttingen
Pulse-coupled oscillators constitute a paradigmatic class of dynamical
systems interacting on networks because they model a variety of biological
systems including flashing fireflies and chirping crickets as well as
pacemaker cells of the heart and neural networks. Synchronization is one
of the most simple and most prevailing kinds of collective dynamics on
such networks.
Here we study collective synchronization of pulse-coupled oscillators interacting
on asymmetric random networks. Using random matrix theory
we accurately predict the speed of synchronization in such networks in
dependence on the dynamical and network parameters [1]. As might be
expected, the speed of synchronization increases with increasing coupling
strengths. Surprisingly, however, it stays finite even for infinitely strong
interactions. Our results indicate that the speed of synchronization is
limited by the connectivity of the network.
[1] M. Timme, F. Wolf, and T. Geisel, cond-mat/0306512 (2003).
DY 21.4 Di 11:00 H3
A statistical mechanics approach to approximate analytical
Bootstrap averages — •Dörthe Malzahn 1 and Manfred Opper
2 — 1 Institut für Mathematische Stochastik, Universität Karlsruhe,
76128 Karlsruhe — 2 Neural Computing Research Group, Aston University,
Birmingham B4 7ET, United Kingdom
Information processing systems are often described by models with a
large number of degrees of freedom which interact by a random energy
function. We consider the problem of learning from example data where
the randomness is induced by the data. Bootstrap is a general method
to evaluate the average learning performance. It estimates averages over