Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Mittwoch
DY 34 Nonlinear Dynamics and Chaos I
Zeit: Mittwoch 14:30–16:30 Raum: H2
DY 34.1 Mi 14:30 H2
Angewandte Verkehrsprognose - ein multimodaler Ansatz im
Betrieb — •Roland Chrobok, Sigurdur F. Hafstein, Florian
Mazur, Andreas Pottmeier und Michael Schreckenberg
— Universität Duisburg-Essen, Physik von Transport und Verkehr, Lotharstr.
1, 47048 Duisburg
Verschiedene Ansätze sind in der Vergangenheit unternommen worden,
Verkehr zu prognostizieren. Bei der Wahl des richtigen Prognosemodells
spielt der Prognosehorizont eine entscheidende Bedeutung. Für langfristige
Prognosen über Jahrzehnte, wie sie in der Verkehrsplanung von Bedeutung
sind, müssen gewisse Annahmen über Bevölkerungsentwicklung
und Wirtschaftswachstum getroffen werden. Für mittelfristige Prognosen
über Tage, Wochen und Monate, wie sie zur Reiseplanung herangezogen
werden, haben sich Heuristiken, also Erfahrungswerte, bewährt. Bei
Kurzfristprognosen über einen Zeitraum von einigen Minuten bis hin zu
mehreren Stunden gewinnt die Kenntnis über den aktuellen Verkehrszustand
an Bedeutung. Phasenraummodelle, parametrisierte Regression
oder verwandte Verfahren sind in vielen Bereichen im Einsatz.
Vorgestellt wird ein multimodaler Ansatz zur Mittel- und Kurzfristprognose,
wie er in einem viel benutzten Verkehrsinformationssystem
verwendet wird. Hauptaugenmerk liegt neben der Prognosegenauigkeit
und der variablen Wahl des Prognosehorizontes auf der praktikablen Implementierung
und der ökonomischen Anwendbarkeit.
DY 34.2 Mi 14:45 H2
Latency effects in time-delay feedback control of chaos —
•Philipp Hövel 1 , Eckehard Schöll 1 , Joshua E. S. Socolar 2 ,
and Wolfram Just 3 — 1 Technische Universität Berlin, 10623 Berlin,
Germany — 2 Duke University, Durham, North Carolina, USA —
3 Queen Mary/ University of London, London, UK
Unstable periodic orbits can be controlled by time-delay feedback
methods. We present a stability analysis in the case of extended timedelay
autosynchronization. Our analysis includes effects of non-zero latency
time, i.e., the time associated with the generation and injection of
the feedback signal. We derive a theoretical explanation for experimentally
observed, nontrivial features of the domain of control, e.g., gaps,
maximum latency times. The explanation is done in the background of
Floquet theory and we take both the unstable eigenmode and a single
stable eigenmode into account.
DY 34.3 Mi 15:00 H2
Minimal model for tag-based cooperation — •Arne Traulsen
and Heinz Georg Schuster — Institut für theoretische Physik und
Astrophysik, Christian-Albrechts Universität, Olshausenstr. 40, 24098
Kiel
Recently, Riolo et al. [Riolo et al., Nature 414, 441 (2001)] showed
by computer simulations that cooperation can arise without reciprocity
when agents donate only to partners who are sufficiently similar to themselves.
One striking outcome of their simulations was the observation that
the number of tolerant agents that support a wide range of players was
not constant in time, but showed characteristic fluctuations. The cause
and robustness of these tides of tolerance remained to be explored. We
clarify the situation by solving a minimal mean-field version of the model
of Riolo et al. [Traulsen and Schuster, Phys. Rev. E. 68, 046129 (2003)].
It allows us to identify a net surplus of random changes from intolerant
to tolerant agents as a necessary mechanism that produces these oscillations
of tolerance, which segregate different agents in time. This provides
a new mechanism for maintaining different agents, i.e., for creating biodiversity.
In our model the transition to the oscillating state is caused
by a saddle node bifurcation. The frequency of the oscillations increases
linearly with the transition rate from tolerant to intolerant agents.
DY 34.4 Mi 15:15 H2
Recovering the dynamical system from short and contaminated
segments of a chaotic trajectory — •Luis Sandoval and Rafael
Gutiérrez — Grupo de Sistemas Complejos, Universidad Antonio
Nariño, Calle 58A 37-94, Bogotá, Colombia
In this work we determine the sufficient characteristics of a trajectory
segment of known chaotic attractors to recover the corresponding dynamical
model. The sufficient conditions correspond to: the size of the
trajectory segment, the localization of the trajectory segment, and the
density of points or sampling frequency. The contamination and resolution
of the data points make the sufficient conditions vary. The dynamical
models considered have all possible nonlinearities up to order two characterized
by thirty parameters. The values of the parameters are obtained
from each trajectory segment and then compared with the corresponding
values of the known dynamical system with chaotic solutions. In many
cases the chaotic solutions are not very sensitive to variations of some parameter
values making the comparison of similar but different dynamical
systems not well defined in terms of their corresponding chaotic solutions.
We solve this problem by using synchronization and estimation of
dynamical measures.
DY 34.5 Mi 15:30 H2
Retinotopic Projections between Discrete Euclidean Manifolds
— •Martin Güßmann 1 , Axel Pelster 2 , and Günter Wunner 1
— 1 Institut für Theoretische Physik 1, Universität Stuttgart, Pfaffenwaldring
57, D-70550 Stuttgart — 2 Institut für Theoretische Physik,
Freie Universität Berlin, Arnimallee 14, D-14195 Berlin
In the course of ontogenesis of vertebrate animals well-ordered neural
connections are established between retina and tectum, a part of the
brain which plays an important role in processing optical information.
As a result of this self-organization process a retinotopic projection is
formed, i.e. neighbouring retinal cells project onto neighbouring cells of
the tectum. We generalize the model of Ref. [1] to obtain order parameter
equations for the connection strengths between two manifolds of
arbitrary geometry. Here we consider the case of discrete n-dimensional
Euclidean manifolds. For the linear chain we are interested in the question
under which circumstances retinotopic or non-retinotopic modes become
unstable. Furthermore, we investigate the generation of retinotopic projections
between two planes. An important result consists in the fact that
this case cannot be reduced to two linear problems, i.e. there is no trivial
decoupling of the two dimensions. The existence of a potential dynamics
of the order parameters is discussed in detail.
[1] A.F. Häussler and C. von der Malsburg, J. Theoret. Neurobiol. 2, 47
(1983)
DY 34.6 Mi 15:45 H2
Spatio-Temporal Structures in a Biological Model with Delay
and Diffusion — •Martin Ohlerich 1 , Michael Bestehorn 1 und
Elena Grigorieva 2 — 1 Lehrstuhl Theoretische Physik II, BTU Cottbus,
Erich-Weinert Strasse 1, 03046 Cottbus, Germany — 2 Belarus State
University, Department of Physics, 220050 Minsk, Belarus
Pattern formation described by differential-difference equations with
diffusion is investigated. It is shown that an arbitrarily small diffusion
induces space-time turbulence just at instability threshold of the homogeneous
stationary solution. We prove this property deriving a complex
Ginzburg-Landau equation on the basis of normal form analysis.
Well above threshold, such turbulent structures give way to synchronized
states ordered by spirals and targets.
paper submitted to Phys. Rev. E
DY 34.7 Mi 16:00 H2
Synchronisationseffekte in global gekoppelten Netzwerken als
— •Alexander Skupin — Humboldt Universität zu Berlin, Newtonstr.14,
10245 Berlin
Aus biologisch-medizinischer Motivation werden (De)Synchronisationeffekte
in globale gekoppelten Netzwerken untersucht und als Modell eines
an Parkinson erkrankten Thalamus verwendet. Dabei wird ein Vergleich
zwischen dem Phasenoszillatoren-Netzwerk (Kuramoto) und einem
FitzHugh-Nagumo-Netzwerk (FHN) gezogen. In beiden Fällen werden
Ordnungsparameter Z eingeführt und die Wirkung eines externes Signal
(Stimulus) auf diese gezeigt. Damit wird im Kuramotomodell ein optimaler
Stimulus zur Desynchronisation gesucht und das Verhalten des
FHN-Netzwerk auf diesen untersucht.
DY 34.8 Mi 16:15 H2
Synchronization of Random Walks with Reflecting Boundaries
— •Andreas Ruttor, Georg Reents, and Wolfgang Kinzel —
Institut für Theoretische Physik, Universität Würzburg, Am Hubland,
97074 Würzburg
Neural networks can synchronize by mutual learning. If the learning