Nonlinear Dynamics at the Free University Berlin

Summer 2020

Oberseminar Nonlinear Dynamics



Tuesday, April 28 Markus Kantner (WIAS Berlin) Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions
Because of the current Corona virus situation, the event will take place online.
Tuesday, May 5 Carlos Rocha (Instituto Superior Tecnico, Lisboa, Portugal) Meanders, zero numbers and the cell structure of Sturm global attractors
We overview recent results on the geometric and combinatorial characterization of global attractors of semiflows generated by scalar semilinear partial parabolic differential equations under Neumann boundary conditions. This is a joint work with B. Fiedler.

Zoom link
Tuesday, May 12 Kostya Blyuss (University of Sussex, England) Mathematical models of epidemics: Insight for control of COVID-19
Zoom link
Tuesday, May 19 Bernold Fiedler (FU Berlin) Reaction, di ffusion, and advection in one space dimension - an introduction
Online talk in the Lisbon WADE - Webinar in Analysis and Differential Equations, 17:00 s.t. Berlin time. Zoom link
Tuesday, May 26th Eckehard Schöll (TU Berlin) Partial synchronization patterns in the brain
The event will take place via Zoom
Tuesday, May 9th Peter Koltai (FU Berlin) Reaction coordinates (order parameters) for metastable systems
We consider non-deterministic dynamical systems showing complex metastable behavior but no local separation in fast and slow coordinates. We raise the question whether and when such systems exhibit a low-dimensional parametrization supporting their effective statistical dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates (or order parameters), such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus less prone to the curse of dimension with respect to the state space of the dynamics than global methods. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as −but not only −molecular dynamics.
Tuesday, June 16 Sindre W. Haugland (TU München) A hierarchy of symmetries: Coexistence patterns of four (and more) Stuart-Landau oscillators with nonlinear global coupling
The symmetry of a system of globally coupled identical units is high: For any solution, interchanging the behavior of any two elements still guarantees a solution. A full N! permutations are possible in total, either not changing the current solution or producing a mirror-image equivalent in phase space. Together, these N! permutations form a symmetry group with many subgroups. Thus, a large number of different partially symmetric solutions might in principle exist. Here, we study N=4 Stuart-Landau oscillators with a particularly intriguing form of global coupling. Its solutions indeed exhibit symmetries corresponding to many of the subgroups of the group of all permutations. Moreover, the transitions between these solutions, together with additional bifurcations more subtly influcencing the symmetry, form an intriguing interconnected hierarchy of differentiated oscillator dynamics. We will also take a brief look at how this hierarchy develops if the ensemble size is scaled up.
Tuesday, June 30 Nicolas Perkowski (FU Berlin) Infinite regularization by noise
It is a very classical yet still surprising result that noise can have a regularizing effect on differential equations. For example, adding a Brownian motion to an ODE with bounded and measurable vector field leads to a well posed equation with Lipschitz continuous flow. While the equation without noise may have none or many solutions. Classical proofs of such results are based on stochastic analysis and on the close link between the Brownian motion and the heat equation. In that derivation it is not obvious which property of the noise gives the regularization. A more recent approach by Catellier and Gubinelli leads to pathwise conditions under which regularization occurs. I will present a simplified version of their approach and use it to construct (very irregular) paths which are infinitely regularizing: after adding them to an ODE we have a unique solution and an infinitely smooth flow - even if the vector field is only a tempered distribution. This is joint work with Fabian Harang.
Tuesday, July 07 Maria Barbarossa (Frankfurt Institute of Advanced Studies) Modeling and simulating the early dynamics of COVID-19 in Germany
Tuesday, July 14 Rico Berner (TU Berlin) From coherence to incoherence: Stability islands in adaptive neuronal networks

Time and Place

Because of the current Corona virus situation, the events take place online.

Guests are always welcome !


switch Last change: Jul. 9, 2020
This page strictly conforms to the XHTMLswitch1.0 standard and uses style sheets. Valid XHTML 1.0! Valid CSS!