| Apr 12, 2012 |
Ali Ahmadi
(FU Berlin) |
Exponential Limit Shadowing Property |
|
In this lecture, we introduce the notion of exponential limit shadowing property and show that this is a persistent property near a hyperbolic set of a dynamical system.
We see that the Omega-stability implies the exponential limit shadowing property and give an example to show that this property is different from limit shadowing.
|
Sergey Tikhomirov
(FU Berlin) |
Shadowing lemma for partially hyperbolic systems |
|
We say that diffeomorphism $f$ of a manifold $M$ is partially
hyperbolic if the tangent bundle of $M$
admits an invariant splitting $E^s + E^c + E^u$
such that $E^s$ and $E^u$ are uniformly hyperbolic and $E^c$ is not.
If $E^c$ is empty, the diffeomorphism is uniformly hyperbolic.
The shadowing lemma says that in hyperbolic systems any pseudotrajectory
can be shadowed by an exact trajectory.
We introduce notion of central pseudotrajectory
and prove that in partially hyperbolic systems any pseudotrajectory
can be shadowed by a central pseudotrajectory.
|
| Apr 19, 2012 |
Brian Smith
(FU Berlin) |
Invariant manifolds for quasilinear parabolic equations |
|
We will investigate the existence of a strongly stable manifold of solutions
for a certain class of quasilinear parabolic equations. The aim is to try
to obtain such a theorem even when there is a null eigenvalue of the
linearized operator involved.
|
| Apr 26, 2012 |
Tuyen Vu Xuan
(FU Berlin) |
Delay-Gleichungen: auf der Suche nach einem globalen Attraktor |
Stefan Liebscher
(FU Berlin) |
The tumbling Universe: Dynamics of Bianchi Models in the Big-Bang Limit |
Bernold Fiedler
(FU Berlin) |
Delayed feedback control of delay equations |
| May 03, 2012 |
N.N. |
t.b.a. |
| May 10, 2012 |
Alan Rendall
(FU Berlin) |
Signalling pathways in T cells and chemical reaction network theory |
|
Chemical reaction network theory (CRNT) is a collection of tools for
understanding the global dynamics of solutions of the type of systems of
ODE which come up in modelling chemical reactions, in particular in
biology. When the tools (such as the deficiency zero theorem) can be applied they give strong results, even for systems with large numbers of unkowns and parameters. The question arises as to how often systems for which CRNT is useful come up in real applications. I will mention a few examples where this is this case, including some arising in T cell signalling.
In particular I will present some work I did recently on a model due to
Salazar and H\"ofer for a signalling pathway involving the transcription
factor NFAT (nuclear factor of activated T cells). This is system of 56
equations with 134 parameters. It can be shown that for any fixed values of the parameters and an obvious conserved quantity this system has a unique stationary solution and that all other solutions converge to it at late times. This model describes only part of the NFAT signalling pathway and I will also describe what happens when it is coupled to a model for another part of the pathway involving calcium oscillations. If time permits I will also indicate how changing the model to explicitly include enzyme concentrations could lead to more complicated dynamics. |
| May 24, 2012 |
Isabelle Schneider
(FU Berlin) |
Stabilization of symmetrically coupled oscillators by time-delayed feedback control |
|
We consider symmetrically coupled oscillators in Hopf normal form. We
focus on the case of three oscillators as the simplest example admitting
nontrivial symmetry.
Our aim is to stabilize the inherently unstable periodic orbits with
discrete rotating wave symmetry. These orbits emerge from a symmetric
Hopf-bifurcation. Time delayed feedback control (Pyragas control) is
introduced.
Going beyond previous results by Fiedler et al., we use the
spatio-temporal symmetry of the system to establish a noninvasive control
method. For that purpose we introduce symmetry-adapted coordinates.
Due to a suitable control term the symmetric Hopf bifurcation splits into
simple Hopf bifurcations with a two dimensional central manifold. As a
consequence
standard exchange of stability in two dimensions is now applicable.
As a result, we are for the first time able to state explicit analytic
conditions for the stabilization of three oscillators. These conditions
are necessary and sufficient. We distinguish between the sub-and
supercritical cases and within the subcritical case between hard and soft
springs.
|
| May 31, 2012 |
Martin Vaeth
(FU Berlin) |
Introduction to degree theory of function triples |
|
The aim of the talk is to give an introduction to degree theory
with some outlook to recent extensions like degree theory
with Fredholm maps, multivalued maps, and function triples.
Some difficulties in the theory are sketched and some
examples will be given.
|
| Jun 07, 2012 |
|
Poster |
| Jun 14, 2012 |
|
Poster |
| Jun 21, 2012 |
Konstantin Bubolz
(FU Berlin) |
Delay stabilization in coupled oscillator systems |
Anna Karnauhova
(FU Berlin) |
Monotone Lyapunov functions in Bianchi models |
| Jun 28, 2012 |
Mustapha Charafi
(IPP Casablanca) |
Two dimensional mathematical modelling of sediment transport and morphological processes in a free surface flow |
Vu Xuan Tuyen
(FU Berlin) |
Kaplan's first eigenvalue method |
| Jul 02, 2012 |
|
Poster |
| Jul 12, 2012 |
Konstantin Mischaikow |
A combinatorial framework for nonlinear dynamics |
Last change: Oct. 16, 2012
