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.
|Title of host publication||Proceedings of 5th International Electronic Conference on Entropy and Its Applications|
|Number of pages||8|
|Publication status||Published - 17 Nov 2019|
|Event||5th International Electronic Conference on Entropy and Its Applications - |
Duration: 18 Nov 2019 → 30 Nov 2019
Conference number: 5
|Name||Sciforum Electronic Conference Series|
|Conference||5th International Electronic Conference on Entropy and Its Applications|
|Period||18/11/19 → 30/11/19|
Bibliographical noteThis 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/).
- Stochastic resonance
- Fokker-Planck equation
- Probability density function
- Information geometry
- Information length
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.