Research

Research Interests

• delay differential equations (focus: state-dependent delay)


• functional differential equations


• invariant manifolds


• qualitative analysis of differential equations


• traffic modeling

Projekte

• German-Russian Interdisciplinary Science Center


• Special issue ''Differential equations with state-dependent delays'' of the Journal Discrete and Continuous Dynamical Systems - Series S
  (jointly with Bernhard Lani-Wayda (University of Giessen) and Qingwen Hu (University of Texas at Dallas))
  To appear in summer 2017.

Preprints

• On a car-following model: Stop and Go solutions obtained by a degenerate Hopf bifurcation of a delay differential equations


• On a car-following model: the model, its constant speed solutions, and their stability

Publications

• On a delay differential equation arising from a car-following model: Wavefront solutions with constant-speed and their stability
  To appear in Discrete and Continuous Dynamical Systems - Series B.
  Preprint available at HBAM 2016-24  bzw.  arXiv:1609.06873.


• On differential equations with state-dependent delay: The principles of linearized stability and instability revisited
  Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2016, no. 81, 17 pp.
  DOI: 10.14232/ejqtde.2016.1.81 (Link)
  


• Multiple slowly oscillating periodic solutions for x'(t)=f(x(t-1)) with negative feedback
  Coauthor: Benjamin B. Kennedy
  Annales Polonici Mathematici 118 (2016), 113 -- 140.
  DOI: 10.4064/ap3899-10-2016 (Link)
  Preprint available at HBAM 2015-43  or  arXiv:1512.09174


• A note on local center manifolds for differential equations with state-dependent delay
  Differential and Integral Equations 29 (2016), 1093 - 1106. (Link)
  Preprint available at HBAM 2015-17  or  arXiv:1503.08811


• Local stability analysis of differential equations with state-dependent delay
  Discrete and Continuous Dynamical Systems - Series A, Vol. 36, No. 6, 3445 - 3461, 2015.
  DOI: 10.3934/dcds.2016.36.3445 (Link)
  Preprint available at HBAM 2015-07  or   arXiv:1502.03142


• Attraction property of local center-unstable manifolds for differential equations with state-dependent delay
  Electronic Journal of Qualitative Theory of Differential Equations 2015, No. 4, 1 - 45, 2015. (Link)


• On a differential equation with state-dependent delay: A center-unstable manifold connecting an equilibrium and a periodic orbit
  Journal of Dynamics and Differential Equations, Vol. 24, No. 2, 197 - 248, 2012.
  DOI: 10.1007/s10884-012-9245-6 (Link)


• The existence and $C^{1}$-smoothness of local center-unstable manifolds for differential equations with state-dependent delay
  Rostocker Mathematisches Kolloquium, 66, 3 - 44, 2011. (Link)

Theses

• On a differential equation with state-dependent delay: A global center-unstable manifold bordered by a periodic orbit
  Doctoral dissertation, University of Hamburg, 2010. (Link)


• Einführung in die Theorie der retardierten Funktionaldifferentialgleichungen anhand eines Verkehrsmodells
  Diploma thesis, University of Hamburg, 2005.

Invited talks

17. Short-term fluctuations of a price model with state-dependent delay
    Scientific seminar on Differential and Functional Differential Equations of the Faculty of physico-mathematical and natural sciences
    Peoples's Friendship University of Russia in Moscow, November 2016


16. On a delay differential equation arising from a car-following model
    Workshop: Dynamics of Delay Equations, Theory and Applications
    Weierstrass Institute for Applied Analysis and Stochstics, October 12-14, 2016


15. On some constant-speed and stop-and-go solutions of a car-following model
    Special Session "Traffic Flow Models and Their Application in Traffic Engineering" of the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    Orlando, July 2016


14. On periodic orbits of exchange rate equations with state-dependent delay
    Section "Differential Equations and Applications" at the Annual Meeting 2015 of the Deutsche Mathematiker-Vereinigung
    University of Hamburg, September 2015


13. Local stability analysis of differential equations with state-dependent delay
    Minisymposium "Delay Differential Equations" of the Equadiff 2015 conference
    Universitáe Claude Bernard Lyon 1, July 2015


12. Attraction property of local center-unstable manifolds for differential equations with state-dependent delay
    7th International Conference on Differential and Functional Differential Equations "DFDE 2014"
    Peoples' Friendship University of Russia in Moscow, August 2014 -- cancelled due to illness


11. Einige Lösungen in Form von Wellenfronten für ein "car-following"-Verkehrsmodell
    Joint seminar in Dynamical Systems of the University of Hamburg, the Institute of Mechanics and Ocean Engineering of the Hamburg University of Technology, and of the MPY-Group at DESY
    Deutsches Elektronen-Synchrotron, July 2014


10. Attraction property of local center-unstable manifolds for differential equations with state-dependent delay
    Special Session "Delay Differential Equations" of the 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    Insituto de Ciencias Matemáticas and Universidad Autónoma de Madrid, July 2014


9. On the existence of periodic solutions for a differential equation with state-dependent delay
   Oberseminar Analysis of the Dept. of Mathematics
   Dresden University of Technology, June 2013


8. The existence and $C^1$-smoothness of local center-unstable manifolds for differential equations with state-dependent delay
   International workshop "Spatio-temporal dynamical systems"
   Steklov Mathematical Institute in Moscow, August 2011


7. Slowly oscillating periodic solutions of a delay differential equation
   Minisymposium "Delay Differential Equations" of the Equadiff 2011 conference
   Loughborough University, August 2011


6. Einige Anmerkungen zur Theorie und zu ausgewählten Beispielen von verzögerten Differentialgleichungen
   Joint seminar in Dynamical Systems of the University of Hamburg, the Institute of Mechanics and Ocean Engineering of the Hamburg University of Technology, and of the MPY-Group at DESY.
   Deutsches Elektronen-Synchrotron, July 2010


5. A center-unstable manifold connecting an equilibrium to a periodic orbit for a differential equation with delay
   Kandidatenseminar of the Research Group Analysis of the Mathematical Institute
   Justus-Liebig University Giessen, May 2010


4. A periodic orbit of a differential equation with state-dependent delay
   Special Session "Delay Differential Equations" of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
   Dresden University of Technology, May 2010


3. Slowly oscillating solutions of a differential equation with state-dependent delay
   Seminar in Analysis of the Dept. of Mathematics
   University of West Bohemia in Pilsen, November 2009


2. Existence and structure of slowly oscillating solutions of a differential equation with state-dependent delay
   Mathematics Colloquium of the Institute for Mathematics
   University of Rostock, January 2009


1. Slowly oscillating (periodic) solutions of a differential equation with state-dependent delay
   Kandidatenseminar of the Research Group Analysis of the Dept. of Mathematics
   Justus-Liebig University Giessen, January 2008