### Abstract

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−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 A necessary 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)=∫[∫(∂
_{t}
p)
^{2}
∕pdx]
^{1∕2}
dt, 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.

Original language | English |
---|---|

Pages (from-to) | 1313-1322 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 525 |

Early online date | 6 Apr 2019 |

DOIs | |

Publication status | Published - 1 Jul 2019 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*525*, 1313-1322. https://doi.org/10.1016/j.physa.2019.04.074

**Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance.** / Hollerbach, Rainer; Kim, Eun jin; Mahi, Yanis.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 525, pp. 1313-1322. https://doi.org/10.1016/j.physa.2019.04.074

}

TY - JOUR

T1 - Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance

AU - Hollerbach, Rainer

AU - Kim, Eun jin

AU - Mahi, Yanis

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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−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 A necessary 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)=∫[∫(∂ t p) 2 ∕pdx] 1∕2 dt, 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.

AB - 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−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 A necessary 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)=∫[∫(∂ t p) 2 ∕pdx] 1∕2 dt, 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.

KW - Fokker–Planck equation

KW - Information geometry

KW - Probability density function

KW - Stochastic resonance

UR - http://www.scopus.com/inward/record.url?scp=85064148343&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2019.04.074

DO - 10.1016/j.physa.2019.04.074

M3 - Article

VL - 525

SP - 1313

EP - 1322

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -