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 journalArticle

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

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
Volume525
Early online date6 Apr 2019
DOIs
Publication statusPublished - 1 Jul 2019
Externally publishedYes

Fingerprint

Stochastic Resonance
Diagnostics
Fokker-Planck Equation
Forcing
Jump
Probability density function
Saturation
Modulation
Numerical Solution
Model
Tend
causes
probability density functions
Necessary
escape
Zero
saturation

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance. / Hollerbach, Rainer; Kim, Eun jin; Mahi, Yanis.

In: Physica A: Statistical Mechanics and its Applications, Vol. 525, 01.07.2019, p. 1313-1322.

Research output: Contribution to journalArticle

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