Amidst the strange vicissitudes of life,'Tis likely, most unlikely things should happen.*

Random Dynamical Systems
and Stochastic Processes in the Sciences

Faculty of Mathematics
University of Bielefeld

Research Group

Barbara Gentz

Daniel Altemeier
Diana Kämpfe
Christian Wiesel

Former Group Members

Kilian Raschel
Felipe Torres
Julian Tugaut

Topics

Dynamical systems are often modelled by differential or partial differential equations. In many situations, random fluctuations either present in Nature or representing the unresolved degrees of freedom, cannot be neglected as they may drastically change the system's behaviour. For instance, in multistable systems arbitrarily small random fluctuations can enable transitions between stable states which would not be possible in the absence of noise. Whether such transitions are observed will depend on the timescale of interest. The related concepts of phase transition, metastability and metastable timescales have been developed in the context of statistical-mechanics type models.


Mixed-mode oscillations in a noisy system

A different approach to random dynamical systems relies on concepts of stability and random attractors which are inspired by the analogous concepts for classical dynamical systems. The corresponding theory of bifurcations in random dynamical systems is still under development.

Activities

Sixth Workshop on Random Dynamical Systems
Bielefeld, 31 Oct–2 Nov 2013

European Women in Mathematics
German Chapter
Conference 2012

Bielefeld, 1–2 Nov 2012

Fifth Workshop on Random Dynamical Systems
Bielefeld, 4–5 Oct 2012

Workshop on Stochastic Dynamics in Mathematics, Physics and Engineering
ZIF, Bielefeld, 2–4 November 2011

Mini-Workshop on Dynamics of Stochastic Systems and their Approximation
MFO, Oberwolfach, 21–27 Aug 2011

ICIAM
Mini-Symposium "Perspectives in Stochastic Dynamics"
Vancouver, BC, 18–22 July 2011

Fourth Workshop on Random Dynamical Systems
Bielefeld, 3–5 Nov 2010

Special Afternoon on Mathematics in the Sciences
Bielefeld, 27 Nov 2009

Third Workshop on Random Dynamical Systems
Bielefeld, 18–20 Nov 2009

Second Workshop on Random Dynamical Systems
Bielefeld, 17–19 Nov 2008

First Workshop on Random Dynamical Systems
Bielefeld, 30 Nov–1 Dec 2007