Hollerbach, R, Kim, E-J and Mahi, Y (2019) Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance. Physica A: Statistical Mechanics and its Applications, 525. pp. 1313-1322. ISSN 0378-4371
Abstract
We consider the classical double-well model of stochastic resonance, in which a particle in a potential V(x,t)=[−x2∕2+x4∕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 Anecessary 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)=∫[∫(∂tp)2∕pdx]1∕2dt, 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Published by Elsevier B.V. This is an author produced version of a paper published in Physica A: Statistical Mechanics and its Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Stochastic resonance; Fokker–Planck equation; Probability density function; Information geometry |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Apr 2019 09:09 |
Last Modified: | 06 Apr 2020 00:39 |
Status: | Published |
Publisher: | Elsevier BV |
Identification Number: | 10.1016/j.physa.2019.04.074 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144481 |