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Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals

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  • Nigmatullin, Raoul R.
  • Toboev, Vyacheslav A.
  • Lino, Paolo
  • Maione, Guido

Abstract

It has been shown that many micromotions in the mesoscale region are averaged in accordance with their self-similar (geometrical/dynamical) structure. This distinctive feature helps to reduce a wide set of different micromotions describing relaxation/exchange processes to an averaged collective motion, expressed mathematically in a rather general form. This reduction opens new perspectives in description of different blow-like signals (BLS) in many complex systems. The main characteristic of these signals is a finite duration also when the generalized reduced function is used for their quantitative fitting. As an example, we describe quantitatively available signals that are generated by bronchial asthmatic people, songs by queen bees, and car engine valves operating in the idling regime.

Suggested Citation

  • Nigmatullin, Raoul R. & Toboev, Vyacheslav A. & Lino, Paolo & Maione, Guido, 2015. "Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 166-181.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:166-181
    DOI: 10.1016/j.chaos.2015.03.022
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    References listed on IDEAS

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    1. Nigmatullin, R.R., 2000. "Recognition of nonextensive statistical distributions by the eigencoordinates method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(3), pages 547-565.
    2. Stauffer, Dietrich & Sornette, Didier, 1998. "Log-periodic oscillations for biased diffusion on random lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(3), pages 271-277.
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    1. Nigmatullin, Raoul R. & Vorobev, Artem S. & Nepeina, Kseniia S. & Alexandrov, Pavel N., 2019. "Fractal description of the complex beatings: How to describe quantitatively seismic waves?," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 171-182.
    2. Nigmatullin, Raoul & Sarkar, Samyadip & Biswas, Karabi, 2021. "New class of fractal elements with log-periodic corrections: Confirmation on experimental data," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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