The slow drift (with speed Îµ) of a parameter through a pitchfork bifurcation point, known as the dynamic pitchfork bifurcation, is characterized by a significant delay of the transition from theâ€¦ (More)

We prove a Kramers-type law for metastable transition times for a class of onedimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transitionâ€¦ (More)

We consider slowâ€“fast systems of differential equations, in which both the slow and fast variables are perturbed by additive noise. When the deterministic system admits a uniformly asymptoticallyâ€¦ (More)

We consider the dynamics of a periodic chain ofN coupled overdamped particles under the influence of noise, in the limit of large N . Each particle is subjected to a bistable local potential, to aâ€¦ (More)

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 asymmetric, modulatedâ€¦ (More)

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than theâ€¦ (More)

The Eyringâ€“Kramers law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. In the weak-noise limit, the transition time is to leadingâ€¦ (More)

We investigate the uctuations of the order parameter in the Hoppeld model of spin glasses and neural networks at the critical temperature 1== c = 1. The number of patterns M(N) is allowed to growâ€¦ (More)

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with itsâ€¦ (More)

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 investigating theâ€¦ (More)