Abstract
We consider the classical doublewell model of stochastic resonance, in which a particle in a potential V(x,t)=[−x ^{2} ∕2+x ^{4} ∕4−Asin(ωt)x] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x≈±1. We present direct numerical solutions of the Fokker–Planck equation for the probability density function p(x,t), for ω=10 ^{−2} to 10 ^{−6} , and A∈[0,0.2]. Previous results that stochastic resonance arises if ω matches the average frequency at which the stochastic forcing alone would cause the particle to jump between the wells are quantified. The modulation amplitudes A necessary to achieve essentially 100% saturation of the resonance tend to zero as ω→0. From p(x,t) we next construct the information length L(t)=∫[∫(∂ _{t} p) ^{2} ∕pdx] ^{1∕2} dt, measuring changes in information associated with changes in p. L shows an equally clear signal of the resonance, which can be interpreted in terms of the underlying meaning of L. Finally, we present escape time calculations, where the Fokker–Planck equation is solved only for x≥0, and find that resonance shows up less clearly than in either the original p or L.
Original language  English 

Pages (fromto)  13131322 
Number of pages  10 
Journal  Physica A: Statistical Mechanics and its Applications 
Volume  525 
Early online date  6 Apr 2019 
DOIs  
Publication status  Published  1 Jul 2019 
Externally published  Yes 
Bibliographical note
NOTICE: this is the author’s version of a work that was accepted for publication in Physica A: Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A: Statistical Mechanics and its Applications, 525, (2019) DOI: 10.1016/j.physa.2019.04.074© 2019, Elsevier. Licensed under the Creative Commons AttributionNonCommercialNoDerivatives 4.0 International http://creativecommons.org/licenses/byncnd/4.0/
Keywords
 Fokker–Planck equation
 Information geometry
 Probability density function
 Stochastic resonance
ASJC Scopus subject areas
 Statistics and Probability
 Condensed Matter Physics
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Eunjin Kim
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