Kramers' law for a bistable system with time-delayed noise

D. Goulding, S. Melnik, D. Curtin, T. Piwonski, J. Houlihan, J. P. Gleeson, G. Huyet

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


We demonstrate that the classical Kramers' escape problem can be extended to describe a bistable system under the influence of noise consisting of the superposition of a white Gaussian noise with the same noise delayed by time τ. The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<τ and τ<t<2τ are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than τ, the delayed noise acquires a nonzero mean value and becomes negatively autocorrelated. To account for these effects we define an effective potential and an effective diffusion coefficient of the delayed noise.

Original languageEnglish
Article number031128
Pages (from-to)5
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number3
Publication statusPublished - 25 Sep 2007




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