Nonlinear Dynamics at the Free University Berlin

Summer 2015

Seminar Advanced Topics in Nonlinear Dynamics

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


Apr 16, 2015 Informal Meeting
Suggestions of topics and schedule
Apr 23, 2015 Anna Karnauhova
(Free University Berlin)
The Origin of the Yang-Baxter Equation - Yang's Approach (Reading session)
The aim of the reading session consists in clarifying Yang's approach for obtaining exact results for the many-body problem presented in the following paper: C. N. Yang: "Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction" Phys. Rev. Lett. 19, 1312 - Published 4 December 1967
Apr 30, 2015 Nicola Vassena
(Free University Berlin)
Monomolecular reaction networks: a new proof of flux transitivity
At first, I will briefly recall the flux influence theorem by Fiedler and Mochizuki. It describes, in terms of the network structure only, which reaction rates j' respond to perturbation of a reaction rate j*. This theorem has been proved to be transitive. Since proving this transitivity turned out to be more involved than expected, I will define some new tools for dealing with these particular networks. These tools are related to standard connectivity concepts from graph theory, and Menger's theorem in particular. Using them, I will reformulate the flux influence theorem and prove its transitivity in a simplified way.
May 7, 2015 Mark Curran
(Free University Berlin)
Reaction-Diffusion Equations with Spatially Distributed Hysteresis in Higher Spatial Dimensions
Many chemical and biological processes are modelled by reaction-diffusion equations with a nonlinearity involving hysteresis. In such problems each spatial point can be in one of two configurations and the configuration changes in time via a hysteresis law. Points in different configurations segregate the domain into several subdomains and switching implies that these subdomains are separated by free boundaries. We will discuss how the hysteresis gives rise to a novel type of free boundary evolution.
May 21, 2015 Dominik Otto
(Free University Berlin)
Determining nodes in regulatory networks
Yuya Tokuta
(Free University Berlin)
Bioconvection with non-isotropic lateral taxis generated by Euglena gracilis
Konstantinos Zemas
(Free University Berlin)
Spatially discrete reaction-diffusion equations with discontinuous hysteresis
May 28, 2015 Judith Lehnert
(Technical University Berlin)
Adaptive control of synchronization in delay-coupled networks
The focus of this talk will be on adaptive control methods, which allow for controlling dynamical systems in situations where parameters drift or are unknown. I will suggest two adaptive control schemes to control zero-lag and cluster synchronization in delay-coupled Stuart-Landau oscillators. The first method relies on the adaptation of the phase of the complex coupling strength, while for the second method I adapt the topology of the network in order to reach the target state.
June 4, 2015 Bernhard Brehm
(Free University Berlin)
Expanding measures in Bianchi Class A Cosmologies
We will give a short introduction to the Bianchi system of ODE and recall the estimates derived last time in November, as well as a gentle introduction to some tools about differential forms and measure theory.
Then we will discuss an expanding measure (volume form) for the Bianchi flow and its Poincare-maps. Using November's estimates and the expanding measure, we prove that Lebesgue almost every solution forms particle horizons (in practice, this means that the solution converges almost exponentially fast to the attractor).
June 11, 2015 Phillipo Lappicy
(Free University Berlin)
On the zero number property for singular scalar parabolic equations
One of the main tools to understand the dynamics of scalar parabolic equations is the zero number property. This property dates back to Sturm, and was reformulated by Matano, Angenent, Fiedler and others. More recently, Chen and Polacik proved a version of this property in the case that the equation displays a coefficient which is singular at one boundary point. On this talk, I explain the main ingredient of Angenent's proof (without any singular term) and how this was modified by Polacik (with a singular term). Lastly, I will present how these ideas can be used to prove the case of two singularities.
June 18, 2015 Nicola Vassena
(Free University Berlin)
Monomolecular reaction networks: A new proof of flux transitivity (Poster)
Phillipo Lappicy
(Free University Berlin)
The dynamics of axially symmetric solutions for dissipative parabolic equations on the sphere (Talk)
Nikita Begun
(Free University Berlin)
Stability of hyperbolic attractors (Poster)
Juliette Hell
(Free University Berlin)
Dynamics of the MAPkinase Cascade (Talk)
June 25, 2015 Ignite Talks
We will have a special afternoon filled with ''ignite talks''!
An ignite talk consists of 20 slides which auto-forward every 15 seconds. Hence every talk lasts exactly 5 minutes. The main point is that there will be large breaks between the blocks of multiple ignite talks for personalized and informal follow-up-discussions. We will also provide drinks, small snacks and enough room for the discussion sessions.

Please find our schedule here!
We will collect all the ignite talks on Tuesday, June 23, so that we can prepare the blocks of multiple talks. Please send your slides in PDF format by Monday June 22nd at the latest.

We hope that many of you would like to participate so that there will be a firework of ideas, problems and results which we can discuss!
July 2, 2015 Robert Krehl (FU Berlin)
Das Fucik Spektrum unter verschiedenen Randwertbedingungen
Xiaobei Ma (FU Berlin)
Deciding Hopf Bifurcations by Quantifier Elimination
Sascha Siegmund (FU Berlin)
Different approaches to flux sensitivity analysis in chemical reaction networks
Ismail Yenilmez (FU Berlin)
Weak Solutions of Conservation Laws
Students present their progress in Master/Bachelor Thesis.
July 9, 2015 Dr. Nikita Begun
(Free University Berlin)
Stability of hyperbolic attractors
The dynamical object which we study is a compact invariant set with a suitable hyperbolic structure. Stability of hyperbolic attractors was studied by Pliss and Sell. They assumed that the neutral and the stable linear spaces of the corresponding linearized systems satisfy Lipschitz condition. They showed that if a perturbation is small, then the perturbed system has a hyperbolic attractor KY, which is homeomorphic to the hyperbolic attractor K of the initial system, close to K, and the dynamics on KY is close to the dynamics on K. At the same time, it is known that the Lipschitz property is too strong in the sense that the set of systems without this property is generic. Hence, there was a need to introduce new methods of studying stability of hyperbolic attractors without Lipschitz condition. We will show that even without Lipschitz condition there exists a continuous mapping h such that h(K) = KY.
July 16, 2015 Hannes Stuke
(Free University Berlin)
Attractors, blow-up and real imaginary afterlife
In my talk I will present theorems connecting the attractor and blow-up of solutions in analytic systems. I will discuss the case of the saddle-node bifurcation and indicate how to prove, that for example in the nonlinear heat equation it is possible to continue the solution onto the real axis through imaginary time after blow-up.

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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