Nonlinear Dynamics at the Free University Berlin

Summer 2018

Seminar Advanced Topics in Nonlinear Dynamics

Prof. Dr. Bernold Fiedler, Dr. Isabelle Schneider


19.04.2018 Mark Curran, Freie Universität Berlin The Hysteretic Limit of a Partial Differential Equation with a Small Parameter
We consider a reaction-diffusion equation with an ensemble of hysteresis operators defined at every spatial point. We associated to this PDE in one variable, a system consisting of one PDE and an ensemble of ODEs defined at every spatial point. More specifically, we replace each of the individual hysteresis operators in the original PDE with a Van der Pol oscillator.
26.04.2018 Poster preliminary discussion SFB910
03.05.2018 Paul Diekwisch, Free University Berlin The Global Attractor Conjecture - The subtle difference between global and local asymptotic stability.
Yuya Tokuta, Free University Berlin Turing instability of bioconvection generated by Euglena gracilis
Microorganisms are known to form spatiotemporal patterns similar to those formed in the Rayleigh-Bénard model for thermal convection. Among such, Euglena gracilis form distinct patterns induced by phototaxes and sensitivity to the gradient of the light intensity. Mathematical analysis of patterns under stationary and oscillatory illumination conditions is in progress and we will discuss Turing instability of the system.
17.05.2018 Nicola Vassena, Free University Berlin Sensitivity of Chemical Reaction Networks: metabolite perturbation
In my previous talks we have addressed and analyzed - under various aspects - the network response to small perturbations of REACTION FLUXES, at equilibrium. In the talk of today I will introduce the absolutely new topic of METABOLITE perturbation. We consider namely small perturbations of the metabolite concentration itself and we investigated possible results, as well as underline different and common aspects with the already developed theory.
24.05.2018 Nicola Vassena, Alejandro Lopez Nieto, and Isabelle Schneider (FU Berlin) Spatio-temporal patterns: control, delays, and design
We present our poster for the upcoming review of SFB 910. Everyone is invited to ask question and give constructive criticism!
31.05.2018 Jia-Yuan Dai Stability and delay feedback control of Ginzburg-Landau spiral waves
In my thesis I have proved the existence of countably many bifurcation curves of Ginzburg-Landau spiral waves, and only those waves associated with the principal bifurcation curve are possibly linearly stable; see [1]. In this talk we focus on the principal bifurcation curve, and aim at proving that one-armed spiral waves are linearly stable, while multi-armed spiral waves are linearly unstable. Then we discuss how to stabilize the linearly unstable spiral waves by introducing noninvasive delay feedback control, based on the control triple method in [2]. [1] J.-Y. Dai (2017). Spiral Waves in Circular and Spherical Geometries: The Ginzburg-Landau Paradigm. Dissertation Thesis, Free University of Berlin [2] I. Schneider (2016). Spatio-temporal feedback control of partial differential equations. Dissertation Thesis, Free University of Berlin
14.06.2018 SFB 910: poster presentation practice
28.06.2018 Sarah Loos (Technische Universität Berlin) Stochastic thermodynamics of delayed noisy systems
Stochastic thermodynamics provides a consistent description of a wide class of Langevin systems, but the Markov assumption is often crucial [1]. However, time-delayed feedback control - which commonly arises, e.g., in biological processes and technical applications - renders stochastic dynamics non-Markovian [2]. Therefore, some basic concepts need to be revisited [3]. In this talk, I will first review the Langevin and Fokker-Planck equation, and discuss issues arising in the presence of a time delay. Then I will introduce thermodynamic definitions and discuss the application to delayed systems. To this end, I will also introduce a Markovian embedding technique [4], which is a promising candidate to calculate the total entropy production in non-Markovian systems. [1] U. Seifert, Rep. Prog. Phys. 75, 126001 (2012). [2] S. A. M. Loos and S. H. L. Klapp, PRE 96, 012106 (2017). [3] M. L. Rosinberg, T. Munakata, G. Tarjus, PRE 91, 042114 (2015). [4] A. Crisanti, A. Puglisi, D. Villamaina, PRE 85, 061127 (2012).
12.07.2018 Ismail Yenilmez (FU Berlin) (Free University, Berlin) Dynamical analysis of Keen's model
David Molle (FU Berlin) A Short Summary of my past Talks regarding the sunflower equation
I am going to give a short summary of the formerly presented material for my master thesis regarding the sunflower equation and its global attractor.
Ignacio Gonzalez Betegon (FU Berlin) Generic results in Networks
In this talk I will introduce the main Results of Roman Joly about couple cell Networks. These results hold for a generic subset of vector fields. In infinite dimensional spaces genericity is one of the analogous of almost everywhere. I would like to show some examples where the mentioned results do not hold.
19.07.2018 Babette de Wolff (Universiteit Utrecht) Approximating delay equations by finite dimensional dynamical systems
Delay differential equations (DDEs) are a type of differential equations that can be viewed as infinite dimensional dynamical systems, in the sense that their state space is an infinite dimensional Banach space. In this talk, we study how we can approximate properties of DDEs by finite dimensional dynamical systems. This is for example of interest from a numerical point of view, since a wide range of numerical tools has been developed for the study of finite dimensional dynamical systems. In particular, we look at the pseudospectral method for DDEs, which is a technique that uses to idea of function approximation by polynomials, to approximate the (infinite number of) eigenvalues of DDEs by eigenvalues of ODEs.

Time and Place

Talks usually take place on Thursday at 2:15 p.m.
at the Free University Berlin
Room 140, Arnimallee 7 (rear building), 14195 Berlin.

Guests are always welcome!


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