Nonlinear Dynamics at the Free University Berlin

Winter 2019/2020

Oberseminar Nonlinear Dynamics



Tuesday, October 29th Pavel Gurevich and Hannes Stuke (Freie Universität Berlin) Reinforcement learning
Tuesday, November 5th Phillipo Lappicy (Universidade de Sao Paulo, Freie Universität Berlin) Horava-Lifshitz Gravity: Bifurcations and Chaos
Lorentzian causal structure, general covariance, and scale invariance are first principles that play a key role in the nature of generic spacelike singularities in general relativity. To bring a new perspective on the contributions of these first principles regarding the chaotic aspects of generic singularities, we consider the initial singularity in spatially homogeneous Bianchi type VIII and IX models in Horava-Lifshitz gravity, which replaces relativistic first principles with anisotropic scalings of Lifshitz type. To describe the nature of the initial singularity in these models, we make use of mathematical tools that include symbolic dynamics and chaos. For the present class of models, it is shown that general relativity is a critical case that corresponds to a bifurcation where chaos becomes generic. For different models nearby the general relativistic critical case, Cantor sets and iterate function systems are important for describing the chaotic aspects of generic singularities. This is joint work with Juliette Hell and Claes Uggla.
Tuesday, November 12th Nicolas Perkowski From hopping particles to stochastic PDEs
I will try to give an overview of some of my research interests, focusing on certain a priori ill posed stochastic PDEs and their derivation. An important task in stochastics is to find and construct "universal" models that describe a given phenomenon. For example, any random variable that is given by the superposition of many small independent influences is approximately Gaussian, independently of the concrete nature of the small influences, and therefore we call the Gaussian distribution universal. When trying to derive universal models for phenomena that evolve in space and time, formal calculations often suggest that we should consider nonlinear stochastic PDEs driven by space-time white noise. This is a problem because due to the irregularity of the noise the solution might be too irregular to make sense of the nonlinearities in the equation. But in recent years we found new ways of overcoming these problems, making sense of the equations, and proving their universality in some cases.
Tuesday, November 19th Ralf Toenjes (University of Potsdam) The Constructive Role of Noise in The Dynamics on Network Hubs for Network Synchronization
We describe and analyze a coherence resonance phenomenon for synchronization in bipartite networks of well connected hubs and followers when the hubs are subjected to noise. Using the Ott-Antonsen ansatz for globally coupled phase oscillators the dynamics of the mean fields is described by a low-dimensional system of Langevin equations. Averaging over the fast stochastic dynamics of the hubs yields ordinary differential equations which predict the coherence resonance reasonably well.

Time and Place

Talks usually take place on Tuesday at 3:15 p.m. at Freie Universität Berlin, Arnimallee 3, Room 130, 14195 Berlin.

Tea/coffee will be served at 2:45 136.
Guests are always welcome !


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