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Effects of the Low Frequencies of Noise on On–Off Intermittency

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A bifurcating system subject to multiplicative noise can exhibit on–off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion (N. G. van Kampen, 24, 171 (1976).) for a random noise with arbitrary power spectrum density and we show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed.

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Authors and Affiliations

  1. Laboratoire de Physique Statistique, CNRS UMR 8550, Ecole Normale Supérieure, 24 rue Lhomond, 75005, Paris, France

    Sébastien Aumaître & François Pétrélis

  2. Department of Physics and Astronomy, Haverford College, 370, Lancaster Avenue, Haverford, PA, 19041, USA

    Sébastien Aumaître

  3. Service de Physique Théorique, Centre d’études de Saclay, 91191, Gif–sur–Yvette Cedex, France

    Kirone Mallick

Authors
  1. Sébastien Aumaître
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  2. Kirone Mallick
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  3. François Pétrélis
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Correspondence to François Pétrélis.

Additional information

PACS Number: 05.40.-a, 05.45.-a, 91.25.-r

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Aumaître, S., Mallick, K. & Pétrélis, F. Effects of the Low Frequencies of Noise on On–Off Intermittency. J Stat Phys 123, 909–927 (2006). https://doi.org/10.1007/s10955-006-9116-9

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  • DOI: https://doi.org/10.1007/s10955-006-9116-9

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