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Arnold family in acoustically forced air bubble formation

Author

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  • Piassi, V.S.M.
  • Colli, E.
  • Tufaile, A.
  • Sartorelli, J.C.

Abstract

We applied an integrate-and-fire model with sinusoidal baseline and constant threshold to describe air bubble formation periodically forced by a sound wave. The model is a deterministic one-dimensional system that predicts the instant of a bubble detachment as a function of the previous one and it is able to reproduce long time behavior with great similarity. The changes in the dynamics as the air flow rate varies can be predicted by a curve in the parameter space of the so called Arnold family of circle maps.

Suggested Citation

  • Piassi, V.S.M. & Colli, E. & Tufaile, A. & Sartorelli, J.C., 2009. "Arnold family in acoustically forced air bubble formation," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1041-1049.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1041-1049
    DOI: 10.1016/j.chaos.2008.04.052
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    References listed on IDEAS

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    1. Tufaile, A & Reyes, M.B & Sartorelli, J.C, 2002. "Explosion of chaotic bubbling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 15-24.
    2. Leon Glass, 2001. "Synchronization and rhythmic processes in physiology," Nature, Nature, vol. 410(6825), pages 277-284, March.
    3. Tufaile, A & Sartorelli, J.C, 2000. "Chaotic behavior in bubble formation dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(3), pages 336-346.
    4. Kang, Yan-Mei & Xu, Jian-Xue & Xie, Yong, 2005. "A further insight into stochastic resonance in an integrate-and-fire neuron with noisy periodic input," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 165-170.
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