Nonlinear Dynamics at the Free University Berlin

Winter 2015/16

Oberseminar Nonlinear Dynamics



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,
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).
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.
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.
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.
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.
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 !


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