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Noise effect on statistical properties of type-I intermittency

Author

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  • Krause, Gustavo
  • Elaskar, Sergio
  • del Río, Ezequiel

Abstract

In this work we analyze the noise effect on type-I intermittency, for which we develop a methodology based on a recently proposed technique used to model the reinjection probability density (RPD). This new methodology allows us to study the noise effect on the intermittency statistical properties for relatively large noise strengths in a quadratic map with different reinjection mechanisms. We show that this procedure allows to predict the behavior of the noisy and noiseless system using the results of the M(x) function which is implemented to obtain the RPD function. We also derive an analytical approximation for the probability density of the laminar lengths and we obtain results for the average laminar length. All analytical approaches show a good agreement with the numerical results even though the statistical properties are calculated using either the noisy or noiseless data, however in some cases the description of the noiseless system using the noisy data can be inaccurate. In addition, we show that occasionally the presence of noise could be not detected due to the results behave as they would be corresponding to a noiseless system. This aspect may have important consequences especially when working with experimental data.

Suggested Citation

  • Krause, Gustavo & Elaskar, Sergio & del Río, Ezequiel, 2014. "Noise effect on statistical properties of type-I intermittency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 318-329.
    • Handle: RePEc:eee:phsmap:v:402:y:2014:i:c:p:318-329
    DOI: 10.1016/j.physa.2014.02.008
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    References listed on IDEAS

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    1. Żebrowski, J.J. & Baranowski, R., 2004. "Type I intermittency in nonstationary systems—models and human heart rate variability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 74-83.
    2. Elaskar, Sergio & del Rio, Ezequiel & Donoso, Jose M., 2011. "Reinjection probability density in type-III intermittency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2759-2768.
    3. A. A. Koronovskii & A. E. Hramov, 2008. "Type-II intermittency characteristics in the presence of noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(4), pages 447-452, April.
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    Cited by:

    1. Bashkirtseva, Irina & Ryashko, Lev, 2017. "Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 573-584.

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