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
Daniel Altemeier
Diana Kämpfe
Julian Tugaut
Former Group Members
Selection of Slides
Metastable lifetimes
in coupled random dynamical systems
Opening Workshop for the SAMSI program on Stochastic Dynamics
Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC, 31 August 2009
Random perturbations of dynamical systems
(Final version, 21 August 2007)
1. French Complex Systems Summer School: Theory and Practice
Institut des Systèmes Complexes de Paris – Ile-de-France, Paris, August 2007
Geometric singular perturbation theory: Application to simple stochastic climate models
Workshop: Stochastic Dynamical Systems and Climate Modeling
BIRS, Banff Centre, Banff, 19 April 2007
The effect of noise on slow–fast systems
Mathematics and Statistics Colloquium
University of Texas, Arlington, TX, 2 March 2007
Desynchronisation of coupled bistable oscillators perturbed by additive white noise
Workshop: Numerics and Theory for Stochastic Evolution Equations
University of Bielefeld, 23 November 2006
Metastability in irreversible diffusion processes and stochastic resonance
SIAM Annual Meeting
Boston, MA, 12 July 2006
SIAM Annual Meeting
Boston, MA, 12 July 2006
Residence-time distributions as a measure for stochastic resonance
Period of Concentration: Stochastic Climate Models,
MPI Mathematics in the Sciences, Leipzig, 1 June 2005
Large deviations and Wentzel–Freidlin theory
Colloquium Equations Différentielles Stochastiques
Toulon, 20 October 2003
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.
Workshops
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 Aug – 27 Aug 2011
ICIAM
Mini-Symposium "Perspectives in Stochastic Dynamics"
Vancouver, BC, 18–22 July 2011
Fourth Workshop on Random Dynamical Systems
Bielefeld, 3 Nov – 5 Nov 2010
Special Afternoon on Mathematics in the Sciences
Bielefeld, 27 Nov 2009
Third Workshop on Random Dynamical Systems
Bielefeld, 18 Nov – 20 Nov 2009
Second Workshop on Random Dynamical Systems
Bielefeld, 17 Nov – 19 Nov 2008
First Workshop on Random Dynamical Systems
Bielefeld, 30 Nov – 1 Dec 2007