Information length as a new diagnostic of stochastic resonance

Eun-jin Kim, Rainer Hollerbach

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    Stochastic resonance is a subtle, yet powerful phenomenon in which a noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted a great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence time distributions, and different information theoretic measures. Here, we show that the information length provides a novel method to capture stochastic resonance. The information length measures the total number of statistically different states along the path of a system. Specifically, 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 − A sin(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] and show that the information length shows a very clear signal of the resonance. That is, stochastic resonance is reflected in the total number of different statistical states that a system passes through.
    Original languageEnglish
    Title of host publicationProceedings of 5th International Electronic Conference on Entropy and Its Applications
    PublisherMDPI AG
    Number of pages8
    Publication statusPublished - 17 Nov 2019
    Event5th International Electronic Conference on Entropy and Its Applications -
    Duration: 18 Nov 201930 Nov 2019
    Conference number: 5

    Publication series

    NameSciforum Electronic Conference Series


    Conference5th International Electronic Conference on Entropy and Its Applications
    Abbreviated titleECEA2019
    Internet address

    Bibliographical note

    This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution
    (CC BY) license (


    • Stochastic resonance
    • Fokker-Planck equation
    • Probability density function
    • Information geometry
    • Information length


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