Nonlinear Dynamics at the Free University Berlin

Winter 2013/2014

Seminar Advanced Topics in Nonlinear Dynamics

PD Dr. P. Gurevich, Dr. Stefan Liebscher


Oct 17, 2013 Isabelle Schneider and Matthias Bosewitz
(Free University Berlin)
Time-delayed feedback control design beyond the odd-number limitation
We present a recent paper by K. Pyragas and V. Novicenko where they discuss necessary conditions for successful Pyragas control. The publication continues Hooton and Amann's work on a new odd-number limitation for autonomous dynamical systems. The main tool is the comparison of proportional with time-delayed feedback control.
Oct 24, 2013 Jia-Yuan Dai
(Free University Berlin)
Existence of spiral ansatz for the complex Ginzburg-Landau equation
The purpose of this talk is to find a suitable spiral ansatz for the complex Ginzburg-Landau equation (CGLe) and solve for it. Firstly a proof for existence of a spiral ansatz based on the work of N. Kopell and L. Howard (1981) and J. Greenberg (1982) is presented, and then a spiral ansatz on a sphere, which reduces the CGLe into a non-autonomous ODE system with singularities at north/south poles, is posed and discussed.
Oct 31, 2013 Bernhard Brehm
(Free University Berlin)
Shadowing based analysis of Bianchi 9 vacuum dynamics
Since I have over the years given several talks about Bianchi in the internal seminar, I should provide some context for this talk. I claimed several ``trivial'' qualitative results on Bianchi, which ``ought to be folklore'' and which provide much needed context and motivation for the hard analysis style estimates which I am pursuing. These qualitative results turned out to be not quite as trivial as I had claimed and seem to be not covered in the previous literature. Combined with the usual mission creep found in any study, this let the qualitative shadowing based analysis of Bianchi dynamics grow to its own project, the first fruit of which I am going to present.
Nov 7, 2013 Phillipo Lappicy
(Free University Berlin)
Einstein equations and the black hole problem
In this talk I'll present an overview of the Einstein equations and provide ideas to show its well-posedness. Lastly, I'll state the black hole initial data problem and how to tackle it.
Nov 21, 2013 Antonio Politi
(University of Aberdeen, UK)
Coarsening processes in Discrete Nonlinear Schroedinger-type models
The Discrete Nonlinear Schroedinger equation (DNLSE) is a paradigmatic model used to describe both Bose-Einstein condensates and propagation in waveguides. The DNLSE behaviour is discussed from the point of view of statistical mechanics, with a particular emphasis given to the convergence to the equilibrium state in the regime of the so-called negative (absolute) temperatures. The observed coarsening is studied with the help of simplified models of exclusion-process type.
Nov 21, 2013 Stefan Liebscher
(Free University Berlin)
Geometries of the projective plane
The projective space provides a unified approach to different types of geometries. This can be a great help to our intuition when dealing with problems in (differential) geometry beyond tensor algebra. In this talk with computer experiments I will introduce some of the features of the projective plane and discuss connections to geodesic flows and parallel transport.
Dec 5, 2013 Juliette Hell
(Free University Berlin)
Bistability for MAPkinase dual futile cycle
This is a joint work with Alan Rendall. MAPkinase plays an important role in cell signaling. It is a proteine that undergoes a cascade of phosphorylations. One level of this cascade consists of the dual futile cycle. We prove bistability in the dual futile cycle via cusp-bifurcation both for the Michaelis-Menten-via-mass-action model (MMMA), where enzymes are explicitly included, and the Michaelis-Menten model (MM, which is a singular limit of the MMMA where enzymes are simplified away). This is the first step in order to prove relaxation-oscillations in the complete cascade.
Dec 12, 2013 Atsushi Mochizuki, Bernold Fiedler
(RIKEN, Tokyo; Free University Berlin)
Rate sensitivity analysis of chemical reaction networks: a public discussion
Jan 30, 2014 Mark Curran, Konstantin Bubolz, Anna Karnauhova
(Free University Berlin)
Ongoing research
Jan 30, 2014 Nikita Begun
(Saint-Petersburg State University, Russia)
Perturbations of attractors
Feb 13, 2014 Nikita Begun
(Saint-Petersburg State University, Russia)
One-dimensional chaos in a system with dry friction
We introduce a new analytical method which allows one to find chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. We prove the existence of an infinite set of periodic points of arbitrarily large periods.
Feb 13, 2014 Hannes Stuke
(FU Berlin)
PDE solutions beyond the blow-up
In this talk I attempt to prove two theorems concerning the possibility of analytic continuation of PDE solutions after blow-up: 1. There exists a small neighborhood of the real time axis such that the solution is analytic up to the blow-up. 2. Under relatively moderate assumptions on the blow-up, it is possible to analytically continue beyond the blow-up. If there is still time left, I will outline further results and research directions arising from an interplay of Hardy space theory and semigroups.

Time and Place

Talks usually take place on Thursday at 2:15 p.m.
at the Free University Berlin
Room 140, Arnimallee 7 (rear building), 14195 Berlin.

Guests are always welcome!


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