Nonlinear Dynamics at the Free University Berlin

Winter 2021-2022

Seminar Advanced Delay Equations and Advanced Differential Equations

Prof. Dr. Bernold Fiedler, Alejandro Lopez Nieto


Thursday, October 7th Alejandro López Nieto (Freie Universität Berlin) Global dynamics of delay equations with monotone feedback
Even the simplest of delay differential equations yield extremely intricate, infinite dimensional dynamical systems. In the talk I will present a constructive method for classifying the global dynamics of a scalar delay equation under symmetry and monotone feedback assumptions. If time allows, after the first part of the talk, I will discuss the question of global continuation of periodic solutions in general delay equations with monotone feedback. Any questions and feedback from the audience are extremely welcome and encouraged!
Thursday, October 21st Gentaro Masuda (Freie Universität Berlin) The analytical basis for non-local Floer homology
Recently, the relation between symplectic geometry and delay differential equations has been drawing attention. There is one approach, so-called non-local Floer homology, which would estimate the number of (some) periodic orbits of delay differential equations with constant delays. The construction of Floer homology consists of three parts: Transversality, Compactness, and Gluing. In this talk, we focus on Compactness in the setting of non-local Floer homology and discuss asymptotic convergence of non-local unregularized gradient flow lines.
Thursday, October 28th Bernold Fiedler (Freie Universität Berlin) Real chaos, and complex time
Abstract (PDF)
Thursday, November 4th Dennis Chemnitz (Freie Universität Berlin) Introducing delay increases the frequency of non-homogeneous oscillators
In this talk, I will describe how the introduction of delay increases the frequency of non-homogeneous oscillators. Furthermore, connections of this problem to optimization problems on spaces of measures and linear programming will be explored. This new viewpoint allows both for a simplification of the proof and for generalization to non-periodic orbits, compared to the work from my master thesis.
Thursday, November 11th Alejandro López Nieto (Freie Universität Berlin) The non-wandering set in delay equations with monotone feedback
The role of the non-wandering set in the description of the global dynamics of a dynamical system is fundamental. Particular applications include finding invariant sets, structural stability properties, and the description of bifurcations of global nature. In the talk, I will address the description of the non-wandering set of a delay equation with monotone feedback. The results presented guarantee the structural stability of the global attractor based purely on local analysis of the periodic solutions and equilibria of the system.
Thursday, November 18th Robin Chemnitz (Freie Universität Berlin) Signed sensitivity of Markov chains with application to chemical reaction networks
The most generic dynamic on a network could easily be the probability distribution of a Markov chain. It can be described as a linear ODE without any stochastic framework. In my Master's thesis, I studied the sensitivity of the unique equilibrium of such systems. The results can be used to analyse the sensitivity of equilibria in more complex dynamics on networks.
Thursday, November 25th Dennis Chemnitz (Freie Universität Berlin) Introducing delay increases the frequency of non-homogeneous oscillators
I will continue my previous talk on the influence of delay on the frequency of a specific type of non-homogeneous oscillator. Specifically, I will show how one can reformulate the lemma as an optimal transport problem, based on an idea by Alejandro Kocsard. It turns out that this reformulation simplifies the proof significantly.
Thursday, December 2nd Alejandro Kocsard (Universidade Federal Fluminense) Rotation theory: from the circle to higher dimensions
Rotation theory has its origins in celebrated works of Henri Poincaré on the dynamics of circle homeormorphisms. Invoking ergodic theory techniques, this theory has been considerably extended to non-invertible maps and to homemorphisms in higher dimensional spaces. In this talk we shall start surveying some classical facts about Poincaré theory on the circle and then discuss some more recent results about rotation theory on the 2-dimensional torus.
Thursday, December 9th Danchen He (Freie Universität Berlin) Properties of an epidemic model with control interventions
This time I will tell a story of one type of epidemic model, which is rarely mentioned in previous studies. Then I will give some properties that have been proven and properties that may be proven in the following studies.
Tilman Glorius (Freie Universität Berlin) Period Mismatch in a Pyragas Controlled System
We attempt an initial investigation into a Pyragas controlled system with an incorrect delay, i.e. the delay chosen in the control scheme does not match the period of the target orbit.
Hauke Sprink (Freie Universität Berlin) Stable manifolds for heteroclinic chains in Horava cosmologies
In this talk we give a perspective on results by Liebscher et al who construct stable manifolds for a certain class of heteroclinic chains in the well-known Bianchi model in general relativity. The aim of our work is to obtain similar results in the parameter dependent Bianchi models within HL cosmology.
Thursday, December 16th Phillipo Lappicy (Universidade Federal do Rio de Janeiro) Phillipo Lappicy (Universidade Federal do Rio de Janeiro)
We explicitly construct global attractors of fully nonlinear parabolic equations. The attractors are decomposed as equilibria (time-independent solutions) and heteroclinic orbits (solutions that converge to distinct equilibria backward and forward in time). In particular, we state necessary and sufficient conditions for the occurrence of heteroclinics between hyperbolic equilibria.s
Thursday, January 13th, at 14:15 Berlin time Jia-Yuan Dai (National Chung Hsing University) Selective feedback stabilization of Ginzburg-Landau spiral waves in circular and spherical geometries
The complex Ginzburg-Landau equation serves as a paradigm of pattern formation. Within circular and spherical geometries, the existence and stability property of Ginzburg-Landau spiral waves have already been proved. Since many spiral waves are unstable and thereby rarely visible in experiments and numerical simulation, we aim to selectively stabilize certain significant classes of unstable spiral waves. Our tool for stabilization is the control triple method, which generalizes the celebrated Pyragas control to the setting of PDEs. This is joint work with I. Schneider and B. de Wolff.
Thursday, January 20th Fan Cheng (Free University Berlin) Using curvature flow to prove isoperimetric inequality in space form
In this talk, we want to discuss proving isoperimetric inequality in space form by constructing different curvature flows and showing long-time existence and exponential convergence of the solution to the flow.
Jannik Schlieffen (Free University Berlin) Electrodynamical processes in quantum mechanics
We will compute the self-force of a particle to show how the quantum potential and the self-force share features with each other.
Thursday, January 27th Nicola Vassena (Free University Berlin) Is genericity always generic?
In the applied sciences, a saddle-node bifurcation is often identified with the Jacobian matrix having a zero eigenvalue. The mathematical argument - rarely mentioned - relies on genericity and details or rigorous proofs are even less often presented. For vector fields with a network structure, I want to clarify why a genericity argument is not always reliable. To this purpose, I will present two (counter)examples of equilibria with a singular Jacobian that fail to satisfy the other saddle-node conditions, for any parameters choice.
Thursday, February 10th Jaqueline Mesquita (University of Brasília) Linearized instability principle for neutral FDEs with state-dependent delays
In this talk, we will prove a linearized instability principle for neutral FDEs with state-dependent delays, using invariance of cone. This is joint work with Bernhard Lani-Wayda.

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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