Nonlinear Dynamics at the Free University Berlin

Winter 2020/2021

Seminar Advanced Topics in Nonlinear Dynamics

Prof. Dr. Bernold Fiedler, Dr. Isabelle Schneider


Program

Thursday, November 5th Kick-off meeting Kick-off meeting
After an exceptionally long semester break, let us reconvene online! Since communication was severely hindered by the pandemic, let us start off with a short review of the past months: What did you do (research-wise, conferences, projects, etc)? Give us a short update! Let us also look forward to the upcoming winter semester: What are your plans and goals?
Thursday, November 12th Nicola Vassena (Freie Universität Berlin) Takens-Bogdanov bifurcation in Metabolic Networks
As a close continuation of the talks of last summer semester, in this talk I will focus on detection and characterization of parameters for Takens-Bogdanov bifurcations in metabolic networks.
Thursday, November 19th Isabelle Schneider (Freie Universität Berlin) An introduction to groupoids
As indicated by the -oid suffix, a groupoid is similar to a group. But how exactly? And how does it generalize the group concept? In this talk, I will give a gentle introduction to the theory of groupoids, as well as present some interesting examples.
Thursday, November 26th Robin Chemnitz (Freie Universität Berlin) Spectral Coarse-Graining of SIS-Dynamics on networks
When computing the solutions of epidemic models on networks, the state space quickly becomes unfeasibly large. The dimension of the process can be reduced via linear projections. This talk is about an approach to preserve the behavior of the dynamic as closely as possible under such projections.
Thursday, December 3rd, Hauke Sprink (Freie Universität Berlin) HL Bianchi models: Periodic orbits and boundary cases
This is the defense of my Bachelor thesis. In this thesis I introduce the Kasner map for parameter dependent Bianchi models within Horava-Lifshitz (HL) gravity. I discuss the dynamics of the map for the boundary values of such parameter range and the existence and uniqueness of periodic orbits.
Thursday, December 10th Gentaro Masuda (Freie Universität Berlin) Toward the asymptotic analysis of unregularized gradient flow lines
Floer homology, with the title of "homology", requires quite tough analysis on its basis. We focus on pseudo vector fields "unregularized gradien", proposed by A. Floer in Hamilton Floer homology, and discuss the very first step for extending the framework to delay/non-local dynamical system.
Thursday, December 17th Babette de Wolff (Freie Universität Berlin) The odd-number limitation
Thursday, January 14th Dennis Chemnitz (Freie Universität Berlin) Periodic orbits of a delayed oscillator
In this talk I will introduce a type of delayed oscillator that, to my knowledge, has not gotten a lot of attention in the literature. Furthermore I will show some first results on the existence of periodic orbits of winding number 1 and will present some speculations and conjectures on these oscillators that I was not able to prove yet.
Thursday, January 21st Alejandro López Nieto (Freie Universität Berlin) Global dynamics of delayed harmonic oscillators
Thursday, January 28th Babette de Wolff (Freie Universität Berlin) The Riesz projection for the monodromy operator of a time-periodic DDE
For a compact operator T, we can compute the projection operator on an eigenspace as the residue of the resolvent at the eigenvalue (in this context, the projection operator is sometimes known as the Riesz projection). The advantage of this formalism is that we can compute the projection without having to find an explicit representation of the dual of T. In this talk, I will apply this concept in the context of the monodromy operator of a time-periodic delay differential equation. I will starting by reviewing the main concepts of holomorphic functions taking values in a complex Banach space, and the main concepts of the Riesz projection. Then I will explicitly compute the projection operator for a simple eigenvalue of the monodromy operator, and show how the characteristic equation naturally appears in this setting.
Thursday, February 11th Tilman Glorius (Freie Universität Berlin) Period Mismatch in a Pyragas Controlled System
Si Mohamed Sah (Department of Mechanical and Electrical Engineering, The University of Southern of Denmark) Identification of damping and stiffness from output only data
In this work I plan to identify damping and stiffness from output only data using theoretical techniques. The results of this ongoing project could be helpful in the diagnosis of vibrating structures while they are under continuous operation.
Thursday, February 18th at 14:15 Jia-Yuan Dai (National Center for Theoretical Sciences, Taiwan) Dynamics of a morbidostat for selection of drug-resistant mutants
A morbidostat is a more advanced chemostat device for developing a microbial culture, where continuous amount of an antibiotic drug is injected/diluted when the total microbes is more/less than some threshold value. During the course of evolution, we are interested in which mutants prevail because of their drug resistance. We introduce a system of ODEs with a drug-on-off-condition to model the morbidostat. Then we study the global dynamics and its dependence on the threshold value by the method of Lyapunov functions. This ongoing research is motivated by Prof. Sze-Bi Hsu.
Thursday, February 25th Phillipo Lappicy (Universidade de São Paulo (ICMC), Brazil) Bianchi type VI0 and VII models in Horava-Lifshitz cosmology
After long detours on past talks regarding the discrete dynamics in HL cosmology by means of perturbing the Kasner map, we will focus on the continuous dynamics in this talk. In particular, we will describe the complete asymptotics (alpha and omega limit sets) of the Bianchi type VI0 and VII models in HL cosmology, due to the existence of Lyapunov functions. Lastly, we will propose conjectures for the Bianchi type VIII and IX models.

Time and Place

Talks usually take place on Thursdays at 15:15
due to the current lockdown situation, our meetings will be held through Zoom.
If you wish to participate, please contact Alejandro for further details.

Guests are always welcome!


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