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

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 tau . The distribution of times between two consecutive switches dec...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 76; no. 3 Pt 1; p. 031128
Main Authors Goulding, D, Melnik, S, Curtin, D, Piwonski, T, Houlihan, J, Gleeson, J P, Huyet, G
Format Journal Article
LanguageEnglish
Published United States 01.09.2007
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Abstract 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 tau . The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<tau and tau<t<2tau are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than tau, 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.
AbstractList 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 tau . The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<tau and tau<t<2tau are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than tau, 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.
Author Curtin, D
Houlihan, J
Piwonski, T
Huyet, G
Goulding, D
Melnik, S
Gleeson, J P
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