Universality of residence-time distributions in non-adiabatic stochastic resonance

Nils Berglund (1, 2) , Barbara Gentz (3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]

We present a mathematically rigorous expression for the residence-time distribution of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distribution is close to a periodically modulated exponential one. Remarkably, the periodic modulation is governed by a universal function, depending on a single parameter related to the forcing period. The behaviour of the distribution and its moments is analysed, in particular in the low- and high-frequency limits.

Mots clés: Stochastic resonance; residence-time distribution; noise-induced exit; oscillating barrier; periodic driving; activated escape; metastability; cycling.; cycling

Domaines: Probabilités [math.PR]

Nils Berglund, Barbara Gentz. Universality of residence-time distributions in non-adiabatic stochastic resonance. Europhys. Letters, 2005, 70, pp.1-7. ⟨10.1209/epl/i2004-10472-2⟩. ⟨hal-00003008⟩