Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance

Rainer Hollerbach, Eun jin Kim, Yanis Mahi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
47 Downloads (Pure)


We consider the classical double-well 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 languageEnglish
Pages (from-to)1313-1322
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Early online date6 Apr 2019
Publication statusPublished - 1 Jul 2019
Externally publishedYes

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 Attribution-NonCommercial-NoDerivatives 4.0 International


  • Fokker–Planck equation
  • Information geometry
  • Probability density function
  • Stochastic resonance

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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