Nonlinear Dynamics at the Free University Berlin

Summer 2016

Oberseminar Nonlinear Dynamics



April 26, 2016 SFB 647
May 3, 2016 Cancelled
May 10, 2016 Martin Väth
(Free University Berlin)
A Primer on Nonlinear Scalar Conservation Laws
The talk is an introduction and survey on basic properties of scalar conservation laws with emphasis on Burgers' equation. It covers an explanation for the formation of shocks, the introduction of weak solutions and the associated “jump condition”, a discussion of rarefactions and how to overcome them with an entropy condition.
May 17, 2016 Björn de Rijk
(Universiteit Leiden, The Nederlands)
Factorization of the Evans function via the Riccati transformation
In the spectral stability analysis of pattern solutions, the presence of a small parameter can reduce the complexity of the linear stability problem. The spectrum of the linearization about certain type of patterns is given by the zero set of an analytic function, the so-called Evans function. Our reduction method yields a factorization of the Evans function in accordance with the scale separation induced by the small parameter. For some specific equations this product structure has yet been established by geometric arguments. Our analytic method formalizes and generalizes the factorization procedure. The main tool for the reduction is the Riccati transformation. We employ our techniques to study the stability of stationary, spatially periodic pulse patterns to a general class of singularly perturbed reaction-diffusion systems. Our Evans-function analysis complemented with a careful analysis of the spectral curve attached to the origin leads to explicit conditions for nonlinear diffusive stability.
May 24, 2016 SFB 647
June 2, 4:15 p.m. 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.stability.
June 7, 2016 Cancelled
June 14, 2016 Cancelled
June 21, 2016 SFB 647
June 28, 2016 Yuri Maistrenko (TU Berlin & National Academy of Sciences of Ukraine) Solitary states in coupled oscillators
Ensembles of identical oscillators can display remarkable spatial or spatiotemporal patterns, so-called solitary states, in which one or a few oscillators split off and behave differently than the others synchronized. At further variations of a control parameter, more and more oscillators leave the coherent cluster manifesting eventually the phenomenon of spatial chaos. Due to these peculiar properties, solitary states can signal to a new scenario for coherence-incoherence transition different from the chimera states.
In the talk, the solitary state appearance is reported for Kuramoto model with attractive and repulsive interactions [1], for non-locally coupled Kuramoto model with inertia [2-3] and Hansel-Mato- Maunier model, as well as for a nonlinear delayed-feedback system ([4]).

[1] Yu.Maistrenko, B.Penkovsky, and M.Rosenblum. Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions. Phys.Rev. E 89, 060901(R) (2014).
[2] T.Kapitaniak, P.Kuzma, J.Wojewoda, K.Czolczynski, and Yu.Maistrenko. Imperfect chimera states for coupled pendula. Scientific Reports 4, 6379 (2014).
[3] P.Jaros, Yu.Maistrenko, and T.Kapitaniak. Chimera states on the route from coherence to rotating waves. Phys. Rev. E 91, 022907 (2015).
[4] V.Semenov, A.Zakharova, Yu.Maistrenko, and E.Schöll. Delayed-feedback chimera states: Forced multiclusters and stochastic resonance. (2016).
3h15 p.m. at Weierstraß Institute Ehrhard-Schmid-Hörsaal, Mohrenstr. 39, 10117 Berlin
Mike Field (Marie Curie Fellow, Imperial College; Research Professor, Rice University) Functional Asynchronous Networks: Factorization of Dynamics and Function
We describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional asynchronous networks gives a description of dynamics and function in terms of properties of constituent subnetworks. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network and thereby answer a question originally raised by Alon in the context of biological networks:
“Ideally, we would like to understand the dynamics of the entire network based on the dynamics of the individual building blocks.”
(page 27, An Introduction to Systems Biology, Uri Alon.)
4h15 p.m. at Weierstraß Institute Ehrhard-Schmid-Hörsaal, Mohrenstr. 39, 10117 Berlin
July 5, 2016
July 12, 2016 SFB 647

Time and Place

Talks usually take place on Tuesday at 3:15 p.m.
at the Free University Berlin
Arnimallee 3 (rear building), room 130.

Tea/coffee at 2:45 p.m.
Arnimallee 3 (front building), room 006.
Guests are always welcome !


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