Research Group

Barbara Gentz

Daniel Altemeier
Diana Kämpfe
Julian Tugaut

Former Group Members

Kilian Raschel
Felipe Torres

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

Noise-induced phenomena in slow–fast dynamical systems
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.