41 citations · 41 across the 1 of their papers we have counts for
7 papers
On the noise-induced passage through an unstable periodic orbit I: Two-level model
Nils Berglund, Barbara Gentz
We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when…
Geometric singular perturbation theory for stochastic differential equations
Nils Berglund, Barbara Gentz
We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptot…
Metastability in simple climate models: Pathwise analysis of slowly driven Langevin equations
Nils Berglund, Barbara Gentz
We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend…
Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
Nils Berglund, Barbara Gentz
We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more informati…
The effect of additive noise on dynamical hysteresis
Nils Berglund, Barbara Gentz
We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the fo…
A sample-paths approach to noise-induced synchronization: Stochastic resonance in a double-well potential
Nils Berglund, Barbara Gentz
Additive white noise may significantly increase the response of bistable systems to a periodic driving signal. We consider two classes of double-well potentials, symmetric and asym…