Nonlinear Dynamics at the Free University Berlin

Summer 2016

Seminar Advanced Topics in Nonlinear Dynamics

PD Dr. P. Gurevich, Dr. Juliette Hell, Isabelle Schneider


Apr 21, 2016 Bernhard Brehm (FU Berlin)
Sensitivity of metabolic reaction networks
We study the influence of rate perturbations on reaction fluxes, at steady state, in general metabolic networks. In particular we establish transitivity of flux influence in the presence of multimolecular reactions. We illustrate our results for several variants of the tricarboxylic citric acid cycle (TCAC). The results are joint work with Bernold Fiedler.
Apr 28, 2016 Hannes Stuke (FU Berlin)
Blow-up of traveling wave type
In my talk I will discuss traveling wave solutions with blow-up of the nonlinear heat equation. I want to address the question of the blow-up profile and show, that the traveling waves can be continued after blow-up in complex time. The complex time continuations introduce a Riemann surface of a logarithmic type.
May 12, 2016, 5 p.m. Prof. Dr. Arnd Scheel (University of Minnesota)
Coherent Structures in Nonlocal Equations
I’ll present recent work on pulses and fronts in systems with nonlocal coupling. I’ll first discuss pinning and unpinning of fronts. Near the Maxwell point, that is, when potential energies of the asymptotic states are close, interfaces are often discontinuous and cannot propagate: they are pinned. I’ll describe results that characterize pinning regions in parameter space and and show that speeds obey an unusual but universal µ^{3/2} asymptotic which is different from conventional µ^{1/2} asymptotics in discrete systems. I’ll also give some motivation and speculation how speed asymptotics may depend in a universal fashion on kernel regularity properties. In the second part of the talk, I’ll explore some of the techniques involved in the study of such traveling wave problems. In particular, I’ll explain how ’spatial dynamics’ tools can be ’translated’ to traveling-wave problems that cannot be cast as differential equations in a spatial variable. As an application, I’ll describe the construction of an excitation pulse in a nonlocal FitzHugh-Nagumo equation.

Note that this talk takes place at 17:15 h in EW 202 at TU Berlin as part of the Eugene Wigner Colloquium.
May 19, 2016 Phillipo Lappicy (FU Berlin)
Symmetrization Property for differential equations on the sphere
We are interested in scalar differential equations when the domain is the two dimensional sphere. In particular, how the spherical symmetry of the domain influences the symmetry of solutions. The approach is an attempt to modify the well known moving plane method. We will discuss which results one should expect by imposing certain conditions on solutions. In particular, which conditions should yield axially symmetric solutions.
May 26, 2016 Sylvain Mazas
Polymatics grew from an idea to visualize mathematical concepts, especially prime and composite numbers. It started with doodles on a sketchbook that eventually became 6 meters wide drawings. Being a hobby musician, I looked further into the relation between music and mathematics, and – almost without noticing it – into algorithmic composition. My research is focused on the confrontation of prime numbers and chaos on the one side, composite numbers and harmony on the other side.
I consider myself more an illustrator than a mathematician and my research should be considered an experimental playground. However, unlike many Artists working with mathematics, my goal is not to use mathematics to create Art, but to understand artistic creation.
The drawings and music presented is the result of a one month Artist-residency at GEMAK, The Hague in 2015.

Pictures and videos of the project:
June 2, 2016 Arne Gödeke
Disputation: A one-way function from thermodynamics and applications to cryptography
One-way functions are an essential building block of modern cryptographic systems. Most one-way functions used in practice are based on number theoretic constructions. Struwe and Hungerbühler proposed a new one-way function using the evolution of the heat equation. This construction, its implementation and possible applications will be explained.
Prof. Dr. Alan Rendall (Universität Mainz)
Dynamical systems arising from the Calvin cycle
I will talk about various aspects of the dynamics of ODE models of the Calvin cycle of photosynthesis, based on work done together with Juan Velazquez, Dorothea Möhring and Stefan Disselnkötter. Issues discussed include boundedness, persistence (whether concentrations can tend to zero asymptotically) and existence and stability of steady states. The modelling of this biological system is presented both because of its intrinsic interest and because of the more general insights it provides for the understanding of biochemical processes.
June 9, 2016 Sascha Siegmund
Different approaches to flux sensitivity analysis in chemical reaction networks
Alejandro Lopez Nieto
An approach to spindles on delay equations
Ignacio González Betegón
Introduction to Ramsey Theory and applications
The aim of this talk is to make an introduction to the Ramsey Theory, theme that I have worked in my Bachelor thesis this year. I would like to present some applications of this Theory and it would be interesting to discuss or find further applications related to Differential equations throw this branch of mathematics which tries to find some order in large enough sets.
Daniel Sarmiento Ferrera
Delayed Burger's equation
June 16, 2016 Sarah Loos (TU Berlin)
Probabilistic treatment of steady states of classical overdamped noisy systems with time-delay
We explore possibilities to describe the dynamical behaviour of classical overdamped, noisy systems with a time-delayed feedback force (that depends on the system state at one earlier instant in time t-τ) via probability densities. Due to the non-Markovian character of such systems, there is no standard Fokker-Planck (FP) equation which corresponds to the (delayed) stochastic Langevin equation [1, 2]. In my talk, I will first review earlier theoretical work on how the FP approach for delayed systems yields an infinite hierarchy of coupled differential equations that involves n-time (joint) probability densities depending on an increasing number of instances in time n -> ∞ [1]. Although these equations are not self-sufficient, they are a valuable starting point for approximation schemes. In particular, I will discuss a first order perturbation-theoretical approach [3] and its application to two exemplary systems involving a Brownian particle in a one-dimensional potential with delayed feedback. We compare the perturbation-theoretical results with those from Brownian dynamics simulations of the underlying delayed Langevin equation. Further, we discuss properties of the two-time probability density, an essential ingredient for the first member of the delayed FP equation.

[1] S. Guillouzic et al., Phys. Rev. E 59, 3970 (1999). [2] M. L. Rosinberg et al., Phys. Rev. E 91, 042114 (2015). [3] T. D. Frank, Phys. Rev. E 71, 031106 (2005).
June 23, 2016 Anna Karnauhova
Anosov Diffeomorphisms on Nil- and Infra-Nilmanifolds
Anosov diffeomorphisms are diffeomorphisms for which the whole manifold is a hyperbolic set. It has been conjectured that nil- and infra-nilmanifolds are the only manifolds admitting Anosov diffeomorphisms. We present three guiding examples of Anosov diffeomorphisms: Arnol’d’s cat map living on a two-dimensional torus, Steve Smale’s generalization to nilmanifolds from 1967 and Michael Shub’s generalization of Steve Smale’s example to infra-nilmanifolds from 1969.
2 p.m. Room E.31, Arnimallee 7
Jia-Yuan Dai
Existence of rotating spiral patterns of the complex Ginzburg-Landau equation on 2-spheres.
We show the existence of rotating spiral patterns, defined by a spiral ansatz, of the complex Ginzburg-Landau equation on 2-spheres. In the proof we apply equivariant bifurcation results and study the kernel of the linear variational equation along each bifurcating solution
4 p.m. Room 130, Arnimallee 3
June 30, 2016 Paul Dieckwisch
Bifurcation analysis of Einstein equations
Adem Güngör
The Two-Component Signaling Systems: two response regulator proteins compete for the phosphoryl group
Daniel Lebede
Bifurcations in the MAP kinase cascade
Xiaobei Ma
Analyzing Hopf Bifurcations and Bogdanov-Takens Bifurcations in Chemical Reactions Using Convex Coordinates
David Molle
A Lyapunov function for the delayed sunflower equation
Ismail Yenilmez
Singularities in Burgers' equation
July 7, 2016 Rehearsal talks for the Conference „Patterns of Dynamics“
Jia-Yuan Dai
Existence of rotating spiral patterns of the complex Ginzburg-Landau equation on 2-spheres
Yuya Tokuta
Bioconvection patterns of Euglena gracilis
Phillipo Lappicy
Einstein constraints: A dynamical approach
Nicola Vassena
Monomolecular reaction networks: flux-influenced sets
July 14, 2016 Rehearsal talks for the Conference „Patterns of Dynamics“
Mark Curran
Reaction-diffusion equations with hysteresis in higher spatial dimensions
Hannes Stuke
Blow up and complex time
Anna Karnauhova
Sturm global attractors, seaweed Lie algebras and classical Yang-Baxter equation
Bernhard Brehm
Sensitivity of metabolic reaction networks
Nikita Begun
Dynamics of discrete time systems with the hysteresis stop operator

Time and Place

Talks usually take place on Thursday at 2:15 p.m.
at the Free University Berlin
Room 130, Arnimallee 3 (rear building), 14195 Berlin.

Guests are always welcome!


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