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Vibrational resonance: a study with high-order word-series averaging

A. Murua

A. Murua

Konputazio Zientziak eta A. A. Saila, Informatika FakultateaDonostia–San Sebastián, Spain
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Murua, A.
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J.M. Sanz-Serna

J.M. Sanz-Serna

Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30Leganés (Madrid), Spain
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Sanz-Serna, J.M.
  
Apr 06, 2016
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Published Online: Apr 06, 2016
Page range: 239 - 246
Received: Feb 07, 2016
Accepted: Apr 06, 2016
DOI: https://doi.org/10.21042/AMNS.2016.1.00018
Keywords
© 2016 A. Murua, J.M. Sanz-Serna, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Vibrational resonance. Accurate numerical integrations of the original oscillatory differential equation and of the averaged system based on words with ≤ 2 letters for two different values of the parameter B that measures the amplitude of the background vibration. In each panel the oscillatory solution appears as a band due to its fast dynamics; the averaged solution (in the centre of the band) varies at a much lower rate. A small increase in B from B = 0.52 (top panel) to B = 0.53 (bottom panel) lets the oscillator make substantially wider excursions without having to increment the amplitude A of the applied forcing.
Vibrational resonance. Accurate numerical integrations of the original oscillatory differential equation and of the averaged system based on words with ≤ 2 letters for two different values of the parameter B that measures the amplitude of the background vibration. In each panel the oscillatory solution appears as a band due to its fast dynamics; the averaged solution (in the centre of the band) varies at a much lower rate. A small increase in B from B = 0.52 (top panel) to B = 0.53 (bottom panel) lets the oscillator make substantially wider excursions without having to increment the amplitude A of the applied forcing.

Higher-order averaging

n# n-letter words with fw ≠ 0Error B = 0.52Error B = 0.53
170.2410.431
2350.0800.481
32170.0260.251
41,4070.0180.036
59,3450.0090.015
662,9510.0040.008
7427,8890.0030.005
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English
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Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other
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