1/f noise and anomalous scaling in Lévy noise-driven on–off intermittency. (1st January 2023)

• Record Type: Journal Article
• Authors: van Kan, Adrian; Pétrélis, François
• Is Part Of: Journal of statistical mechanics. (2023:Jan.)
• Publication Date: 2023-01-01
• Subjects: multiplicative Lévy noise -- instability -- on-off intermittency -- first-passage time statistics -- 1/f noise -- anomalous scaling; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/acac71
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: 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.