### 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 language | English |
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Title of host publication | Proceedings of 5th International Electronic Conference on Entropy and Its Applications |

Publisher | MDPI AG |

Number of pages | 8 |

Volume | 5 |

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 https://ecea-5.sciforum.net |

### Publication series

Name | Sciforum Electronic Conference Series |
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Volume | 5 |

### Conference

Conference | 5th International Electronic Conference on Entropy and Its Applications |
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Abbreviated title | ECEA2019 |

Period | 18/11/19 → 30/11/19 |

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 (http://creativecommons.org/licenses/by/4.0/).

### Keywords

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

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## 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.