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Winter 2015/16
Oberseminar Nonlinear Dynamics
Organizers
Program
| Oct 13, 2015 |
SFB 647 |
| Oct 20, 2015 |
CANCELLED |
| Oct 27, 2015 |
CANCELLED |
| Nov 3, 2015 |
Ivan Ovsyannikov
(University of Bremen, Germany) |
Criteria of birth of Lorenz attractors |
The birth of Lorenz attractors is proved for a system which we call
an extended Lorenz model. It appears as a normal form for some class of codimension-three (and codimension-four)
bifurcations. Thus, the proof of the birth of the Lorenz attractor in this model will immediately prove the birth of such
attractor in these bifurcations.
With a transformation of coordinates and parameters the extended Lorenz model can be also transformed to the
original Lorenz equations (for some parameter values it may require time-reversal).
Thus, the proof of an attractor in the extended model gives immediately a Lorenz attractor or repeller in the Lorenz system.
This is a joint work with D. Turaev, http://arxiv.org/abs/1508.07565/.
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| Nov 10, 2015 |
SFB 647 |
| Nov 17, 2015 |
Michael Herrmann
(WWU Münster, Germany) |
Hysteresis in discrete forward-backward diffusion equations |
We study the dynamics of phase interfaces in discrete diffusion equations with bistable nonlinearity. In the first part we identify a
hysteretic free boundary problem for the parabolic scaling limit by combining heuristic arguments with numerical evidence.
Afterwards we discuss the rigoros justification for the bilinear and the trilinear case.
Joint work with Michael Helmers (University of Bonn).
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| Nov 24, 2015 |
Serhiy Yanchuk
(WIAS, Germany) |
Dynamic jittering and spiking solutions in oscillators with pulsatile delayed feedback |
| Oscillatory systems with time-delayed pulsatile feedback appear in various
applied and theoretical research areas, and received a growing interest in recent years. For such systems, we report a
remarkable scenario of destabilization of a periodic regular spiking regime. At the bifurcation point numerous regimes
with nonequal interspike intervals emerge. We show that the number of the emerging, so-called “jittering” regimes grows
exponentially with the delay value. Although this appears as highly degenerate from a dynamical systems viewpoint, the
“multijitter” bifurcation occurs robustly in a large class of systems. We observe it not only in a paradigmatic
phase-reduced model, but also in a simulated Hodgkin-Huxley neuron model and in an experiment with an electronic circuit.
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| Dec 1, 2015 |
Helge Dietert
(University of Cambridge, UK) |
Stability and bifurcation for the Kuramoto model |
The Kuramoto model is a prototype for synchronisation behaviour of heterogeneous
oscillators due to a global coupling. In this model the totally unsynchronised state appears to be stable in simulations with a
large number of oscillators. In order to understand this stability, I will first recall the mean-field (thermodynamic) limit, which
recasts the problem to a PDE on the density of the oscillators. By a careful study of the PDE in Fourier space, we can then
understand the apparent stability through the heterogeneity of the oscillators. With this we can show perturbative and global
stability results and derive a center manifold reduction to determine the bifurcation behaviour. The mathematical structure is
similar to the Vlasov system, where the stability is called Landau damping.
Please note:
Unlike usual, the seminar takes place in the lecture room 4.13, Hausvogteiplatz 11 A.
Please wait at the doorkeeper's Mohrenstrasse 39 (usual location) to get access to the other building.
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| Dec 8, 2015 |
SFB 647 |
| Dec 15, 2015 |
CANCELLED |
| Dec 22, 2015 |
CANCELLED |
| Jan 5, 2016 |
SFB 647 |
| Jan 12, 2016 |
Edgar Knobloch
(University of California at Berkeley, CA/US) |
Spatially localized structures in dissipative systems |
| Spatially localized structures arise frequently in nature.
In this lecture I will describe a number of examples from different physical systems,
followed by a discussion of the basic ideas behind the phenomenon of nonlinear self-localization
that is responsible for their existence. I will illustrate these ideas
using a simple phenomenological model and explain
why the qualitative predictions of this model help us understand
the properties of much more complicated systems exhibiting spatial localization.
|
| Jan 19, 2016 |
Hans-Otto Walther
(Justus Liebig University Giessen, Germany) |
Differential Equations, Delays, and Frechet Manifolds |
For differential equations with bounded state-dependent delay the initial value problem
is well-posed on a submanifold in a Banach space of maps on a compact interval, with all solution operators differentiable,
under mild smoothness hypotheses on the functional defining the differential equation. In the general case, with the delay
not necessarily bounded, a similar result holds provided the
delay is locally bounded. Such results, however, miss
solutions whose histories do not belong to the ambient Banach space of maps on the negative halfline.
This suggests to study the initial value problem for data in the Frechet space of all continuously differentiable maps on the
negative halfline. The lecture presents a result which provides a continuous semiflow on a submanifold of the Frechet space
whose solution operators are continuously differentiable in an appropriate sense.
Please note:
Unlike usual, the seminar takes place at Free University Berlin, Arnimallee 6 (pi building), seminar room 025/026.
Tea/coffee at 2:45 p.m. Arnimallee 3 (front building), room 006.
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| Jan 26, 2016 |
Fredi Tröltzsch
(Technische Universität Berlin, Germany) |
Optimization of nonlocal distributed feedback controllers with time
delay for the Schlögl model |
A class of Pyragas type nonlocal feedback controllers is investigated
for the 1D Schlögl model, a semilinear parabolic equation that is also
known as Nagumo equation. The main goal is to find an optimal kernel
in the controller such that the solution of the controlled equation is
close to a desired spatio-temporal pattern. An optimal kernel is the
solution to a nonlinear optimal control problem with the kernel taken
as control function. The well-posedness of the problem and necessary
optimality conditions are discussed. Special emphasis is laid on time-periodic
target functions. A particular issue is the periodic behavior of
solutions to the feedback equation.
This is joint work with P. Nestler and E. Schöll.
Please note:
Unlike usual, the seminar takes place at Free University Berlin, Arnimallee 6 (pi building), seminar room 025/026.
Tea/coffee at 2:45 p.m. Arnimallee 3 (front building), room 006.
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| Feb 2, 2016 |
SFB 647 |
Time and Place
Talks usually take place on Tuesday at 3:15 p.m.
at the Weierstraß Institute
Ehrhard-Schmid-Hörsaal, Mohrenstr. 39, 10117 Berlin.
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !
Archive
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Last change: Jan. 28, 2016
