Europhys. Lett.
Volume 70, Number 1, April 2005
Page(s) 1 - 7
Section General
Published online 09 March 2005
Europhys. Lett., 70 (1), pp. 1-7 (2005)
DOI: 10.1209/epl/i2004-10472-2

Universality of first-passage- and residence-time distributions in non-adiabatic stochastic resonance

N. Berglund1 and B. Gentz2

1  Centre de Physique Théorique (Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités d'Aix Marseille 1, Aix Marseille 2 et Sud Toulon-Var, affiliée à la FRUMAM.) , CNRS Luminy Case 907, 13288 Marseille Cedex 9, France
2  Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr. 39, 10117 Berlin, Germany

received 16 August 2004; accepted in final form 10 February 2005
published online 9 March 2005

We present mathematically rigorous expressions for the first-passage-time and residence-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distributions are close to periodically modulated exponential ones. Remarkably, the periodic modulations are governed by universal functions, depending on a single parameter related to the forcing period. The behaviour of the distributions and their moments is analysed, in particular in the low- and high-frequency limits.

02.50.Ey - Stochastic processes.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.

© EDP Sciences 2005