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Research

Research Topics

  • Dynamics of Ordinary and Partial Differential Equations
  • Pattern Formation, nonlinear waves, stability
  • Heteroclinic and homoclinic bifurcations
  • Symmetries, Coupled Oscillators
  • Applications

Projects

Selected current grants

DFG Collaborative Research Center SFB TRR 181 “Energy transfers in ocean and atmosphere, project areas first phase M2, second phase M1, M2, M7 [ link https://www.trr-energytransfers.de/ ] associated with MARUM [link https://www.marum.de/index.html]

DFG Research Training Group [\pi^3] “Parameter identification”, project areas first phase R2, second phase R1
[ link https://www.uni-bremen.de/rtg-pi3 ] 

Selected past grants

DFG grant RA 27288/1-1 "Ergodic theory of nonlinear waves in discrete and continuous excitable media” (2016-2020)

“Research orientation in Bsc mathematics (ForMath)", within program “ForstAintegriert” at University of Bremen (2017-2019)

“Stability boundaries of wavetrains” within “Nonlinear dynamics of natural systems (NDNS)" program of the Durch research fund (NWO) (2012-2014)

"Critical transitions and early-warning signals in spatial ecosystems", within complexity program of Durch research fund (NWO) (2011-2015)

 

PhD Dissertations

Miriam Steinherr Zazo:
Bifurcation Analysis for Systems with Piecewise Smooth Nonlinearity and Applications
17.12.2021

Dennis Ulbrich:
Ergodic theory of nonlinear waves in discrete and continuous excitable media
25.08.2021

Jichen Yang:
Diffusion, advection and pattern formation
23.03.2020

Björn de Rijk:
Periodic pulse solutions to slowly nonlinear reaction-diffusion systems 
22.12.2016
with Prof. Arjen Doelman

Eric Siero:
A recipe for desert: Analysis of an extended Klausmeier Model 
09.02.2016
with Prof. Arjen Doelman

Sjors van der Stelt:
Rise and fall of periodic patterns in a generalised Klausmeier-Gray-Scott model
27.01.2012
with Prof. Arjen Doelman

 

 

Current PhD Projects

  • Lars Siemer: Patterns in spintronic decive models: Landau-Lifshitz-Gilert-Slonczewsky equations
  • Artur Prugger: Equatorial quasi-geostrophic balancecs, dissipation and nonlinear waves
  • Paul Holst: Analysis of parameterised PDE models for geophysical flow and climate

Master and Bachelor Theses

B.Sc.: 

09/21 A. Konschin, Randwertprobleme
03/21 S. Suckau, Analytische Methoden zur Untersuchung von Musterbildung in Reaktions-Diffusions-Systemen
08/14 M. Geers, Existenz und Eindeutigkeit bei gewöhnlichen Differentialgleichungen mit nicht-stetigem Vektorfeld 
08/14 I. Gossen, Turing-Instabilitäten in Reaktions-Diffusions-Systemen
08/14 A. Prugger, Satz über die C^k-impliziten Funktionen auf Banachräumen
07/14 H. Myska, Weierstraßscher Vorbereitungssatz und Verwandte 
04/14 M. Hackbusch, Deterministische und stochastische Modelle für die Ausbreitung von Infektionskrankheiten in großen Populationen

M.Sc.: 

04/20 J. Gienapp, Wellendynamik in geostrophen Flüssen
04/19 M. Temmen, Analyse der Stabilität und Steuerung eines 3DOF-Schiffskörpers
08/18 S. Yoldas, Amplitudengleichung des Swift-Hohenberg Modells
02/17 A. Prugger, Flachwassergleichung mit Diffusion: Stabilität und Verzweigung von Wellen
04/16 D. Ulbrich, Topological Entropy and Asymptotic Extinction Rate of the Three-State 1d-Greenberg-Hastings Model
08/11 E. Siero, A H^2 well-posedness result for second order quasilinear parabolic PDE’s on the real line with an application to a generalisation of the Gray-Scott model
09/09 Y. Lesmana, Lyapunov-Schmidt Reduction for Singular Perturbations: Wave Trains in Reaction-Diffusion Systems