Information length as a new diagnostic of stochastic resonance

Eun-jin Kim, Rainer Hollerbach

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

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Abstract

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
Volume5
Publication statusPublished - 17 Nov 2019
Event5th International Electronic Conference on Entropy and Its Applications -
Duration: 18 Nov 201930 Nov 2019
Conference number: 5
https://ecea-5.sciforum.net

Publication series

NameSciforum Electronic Conference Series
Volume5

Conference

Conference5th International Electronic Conference on Entropy and Its Applications
Abbreviated titleECEA2019
Period18/11/1930/11/19
Internet address

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Bibliographical note

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Keywords

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

Cite this

Kim, E., & Hollerbach, R. (2019). Information length as a new diagnostic of stochastic resonance. In Proceedings of 5th International Electronic Conference on Entropy and Its Applications (Vol. 5). (Sciforum Electronic Conference Series; Vol. 5). MDPI AG.