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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2023

1/f noise and anomalous scaling in Lévy noise-driven on–off intermittency

François Pétrélis
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Résumé

On–off intermittency occurs in nonequilibrium physical systems close to bifurcation points, and is characterised by an aperiodic switching between a large-amplitude ‘on’ state and a small-amplitude ‘off’ state. Lévy on–off intermittency is a recently introduced generalisation of on–off intermittency to multiplicative Lévy noise, which depends on a stability parameter α and a skewness parameter β . Here, we derive two novel results on Lévy on–off intermittency by leveraging known exact results on the first-passage time statistics of Lévy flights. First, we compute anomalous critical exponents explicitly as a function of arbitrary Lévy noise parameters ( α , β ) for the first time, by a heuristic method, extending previous results. The predictions are verified using numerical solutions of the fractional Fokker–Planck equation. Second, we derive the power spectrum S ( f ) of Lévy on–off intermittency, and show that it displays a power law S ( f ) ∝ f κ at low frequencies f , where κ ∈ ( − 1 , 0 ) depends on the noise parameters α , β . An explicit expression for κ is obtained in terms of ( α , β ) . The predictions are verified using long time series realisations of Lévy on–off intermittency. Our findings help shed light on instabilities subject to non-equilibrium, power-law-distributed fluctuations, emphasizing that their properties can differ starkly from the case of Gaussian fluctuations.
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Dates et versions

hal-04251769 , version 1 (20-10-2023)

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Adrian van Kan, François Pétrélis. 1/f noise and anomalous scaling in Lévy noise-driven on–off intermittency. Journal of Statistical Mechanics: Theory and Experiment, 2023, 2023 (1), pp.013204. ⟨10.1088/1742-5468/acac71⟩. ⟨hal-04251769⟩
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