| Thursday, October 17th |
Philippo Lappicy (Universidade de Sao Paulo; Universidade de Lisboa) |
A Poincaré compactification (and hope of continuation) of blow-up solutions of parabolic equations |
| The goal of this talk is to compactify the semiflow for parabolic equations when blow-up occurs. We introduce a new notion of Poincaré compactification that allows for a " heigth " function to be spatially dependent (non-homogeneous), and hence different points in the domain are compactified with different rates: the blow-up point is normalized to be one, whereas points nearby are slightly below this value. We will compare such compactification with the previous (homogeneous) one, which was used to study grow-up phenomena by Juliette Hell, Nitsan Ben-Gal and others, and specify the pro's and con's of each method.
On one hand, such compactification (hopefully) provides a new way to continue solutions after blow-up time by means of compactification, differently than the analytic continuation of our complex-time guru Hannes Stuke.
On the other hand, the new compactification provides a global picture of the dynamics outside bounded sets of phase-space. In particular, we seek to compactify the unstable manifold of the trivial equilibria, which was parametrized by Bernold and Matano, and show the structure of its boundary consisting of compactified blow-up profiles.
This is an ongoing discussion with the one and only, Juliana Fernandes Pimentel (UFRJ), and I confess we are still struggling with several aspects of these findings.
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| Thursday, October 24th |
Babette de Wolff (Free University Berlin) |
The odd number limitation and levels of noninvasiveness |
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In this talk, we will study the restrictions and possibilities of time delayed feedback control based on the level of 'noninvasiveness' of a control term.
We start by revisiting the odd number limitation for non-autonomous systems, giving a more geometric approach/proof to this result. We then proceed to make a categorisation of all possible delayed control terms, distinguishing between the control terms where only the period of the target orbit is known and the control terms where more information is used. We then give a full classification of the control terms that only use the period. Moreover, for this class we write down a necessary condition for successful stabilisation, extending earlier results in the literature.
This is joint work with Isabelle Schneider.
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| Thursday, October 31st |
Babette de Wolff (Free University Berlin) |
The odd number limitation and levels of noninvasiveness, part II |
| This is part II of the talk of last week, where we looked at the odd number limitation and distinguished between different control terms based on their 'noninvasiveness'. This week, we will aim to classify the fully noninvasive control terms. Moreover, for this class we write down a necessary condition for successful stabilisation, extending earlier results in the literature.
This is joint work with Isabelle Schneider.
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| Thursday, November 7th |
Maximillian Bee (Free University Berlin) |
Bachelor Thesis: The discrete charm of the Riemann Zeta-function - Geometric Insights Through Analytic Continuation |
| The defense will open with a 15 minute presentation of my thesis' central result: The Riemann Zeta Function's partial sums asymptote a logarithmic spiral in the complex plane for real part greater than zero and in particular a circle for real part equal to 1. The presentation is followed by a 15 minute discussion.
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| Alejandro López Nieto (Free University Berlin |
On the source of periodic orbits in delay monotone feedback systems |
| Steady states and periodic solutions play a cardinal role in the global dynamics of delay equations with monotone feedback. While the first ones don't represent a specially difficult challenge, the generation process of the later is unknown to date.
In the talk I will present a series of examples that hint in the direction of planar-like dynamics being the source of periodic solutions.
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| Thursday, November 14th |
Alejandro López Nieto (Free University Berlin) |
Three examples to understand periodic solutions in delay
monotone feedback systems |
| After a quick total recall, the talk will close the family of examples that were introduced last week.
The main goal is to try to understand the genesis mechanism hidden behind the periodic solutions
of delay monotone feedback systems.
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| Thursday, November 21st |
Jia-Yuan Dai (National Center for Theoretical Sciences Taiwan) |
Spiral waves for competition-diffusion systems of three species |
| For most initial conditions, two competing species cannot coexist, that is, one of them goes extinct
for large time. When another species invades, those three species exhibit an effect of indirect
cooperation, and then coexistence becomes possible. Motivated by numerical evidences, I will
explain how to study the existence problem of coexistence states in a shape of rotating spiral.
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| Thursday, November 28 |
Abderrahim Azouani |
Control of dynamical systems in terms of linear matrix inequalities |
| In this talk, we propose a stability technique of some dynamical systems
to derive sufficient conditions, with an appropriate Lyapunov-Krasovskii
method, in terms of linear matrix inequalities to obtain the same
results as in my previous work with E. Titi. Indeed, this approach can be
extended to the case of the time-varying delay system.
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| Thursday, December 5th |
Isabelle Schneider and Babette de Wolff (Free University Berlin), Phillipo Lappicy (Universidade de Sao Paulo) |
Selective feedback stabilization of Ginzburg-Landau spirals waves
in the spherical geometry |
| In this talk, we will discuss feedback stabilization of spirals in the Ginzburg-Landau equation. This
is ongoing work with Jia-Yuan Dai.
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| Thursday, December 12th |
Gentaro Masudo (Humboldt Universität Berlin) |
Introduction to Symplectic geometry & Hamiltonian dynamics |
| In this talk, we see the basic structure of symplectic geometry and how it is connected to physics.
|
| Thursday, December 19th |
Felix Kemeth
(Fraunhofer IIS) |
Cluster singularity: The unfolding of clustering behavior in globally
coupled Stuart-Landau oscillators |
| The ubiquitous occurrence of oscillatory cluster patterns in nature still lacks a comprehensive understanding. However, the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate clustering dynamics in a mean-coupled ensemble of such limit-cycle oscillators. In particular, we show how clustering occurs in minimal networks and elaborate how the observed 2-cluster states crowd when increasing the number of oscillators. Using persistence, we discuss how this crowding leads to a continuous transition from balanced cluster states to synchronized solutions via the intermediate unbalanced 2-cluster states. These cascade-like transitions emerge from what we call a cluster singularity. At this codimension-2 point, the bifurcations of all 2-cluster states collapse and the stable balanced cluster state bifurcates into the synchronized solution supercritically. We confirm our results using numerical simulations and discuss how our conclusions apply to spatially extended systems.
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| Thursday, January 16th |
Siva Prasad Chakri Dhanakoti
(Free University Berlin) |
Euler's Elastica: An Introduction and Examples |
| Euler's Elastica is useful in modeling large scale elastic deformations in slender structures. It is
a classic example of a bifurcation problem. It can be derived either by minimizing an energy like
functional or by using Newton's law of motion. We will first derive beam-bending equations using
Newton's laws and later extend them to the cases of buckling and large deformations. Then, we
can discuss some examples of bifurcations seen in elastic rods.
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| Thursday, January 23rd |
Dennis Chemnitz (Free University Berlin) |
Proving Sharkovsky's theorem using algebraic methods |
| Sharkovsky's theorem was already proved in 1962 by Sharkovsky himself. However, recently a
more algebraic approach was discovered by Chris Bernhardt. I will give a short explanation of
how this new approach is different to the classic one and what the advantages or disadvantages
might be.
|
| David Molle (Free University Berlin |
The sunflower and Liénard - a short review and example(s) |
| I will give a short review on my last talk and look at one or two example(s).
|
| Hauke Sprink (Free University Berlin |
HL Bianchi models: the boundary cases |
| In this talk I will give a short introduction to parameter dependent Bianchi models within Horava-
Lifshitz (HL) gravity, and discuss the dynamical behaviour for the boundary values of such parameter
range.
|
| Tilman Glorius (Free University Berlin |
TBA |
| Thursday, January 30th |
Dennis Chemnitz (Free University Berlin) |
Proving Sharkovsky's theorem using algebraic methods |
| Sharkovsky's theorem was already proved in 1962 by Sharkovsky himself. However, recently a
more algebraic approach was discovered by Chris Bernhardt. I will give a short explanation of
how this new approach is different to the classic one and what the advantages or disadvantages
might be.
|
| Siva Prasad Chakri Dhanakoti (Free University Berlin |
Euler's Elastica: An Introduction and Examples - Part II |
| We continue the previous talk on Euler's Elastica. Euler's Elastica is useful in modeling large scale elastic deformations in slender structures. It is a classic example of a bifurcation problem. It can be derived either by minimizing an energy like functional or by using Newton's law of motion. We will first derive beam-bending equations using Newton's laws and later extend them to the cases of buckling and large deformations. Then, we can discuss some examples of bifurcations seen in elastic rods.
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| Thursday, February 6th |
Dennis Chemnitz (Free University Berlin |
A very short introduction to algebraic topology |
| It is not uncommon to use methods of algebraic topology when trying to prove statements about dynamical systems. One such example would be Conley index theory. In this talk I will introduce some basic concepts of algebraic topology like singular homology and show how they can be used to prove some well known theorems like for example Brouwers fixed point theorem.
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Last change: Feb. 4, 2020
