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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…
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…
Pathwise description of dynamic pitchfork bifurcations with additive noise
Nils Berglund, Barbara Gentz
The slow drift (with speed $\eps$) of a parameter through a pitchfork bifurcation point, known as the dynamic pitchfork bifurcation, is characterized by a significant delay of the…