2006/05/01 by Sébastien Aumaître, Sebastien Aumaitre, Kirone Mallick +2 · 1 citation
Economics, Econometrics and Finance · Environmental Science · Mathematics · Physics and Astronomy · #Algorithm #Chaotic #Colors of noise #Complex Systems and Time Series Analysis #Computer science #Ecosystem dynamics and resilience #Gaussian #Gaussian noise #Instability #Intermittency #Mathematical analysis #Mathematics #Multiplicative function #Multiplicative noise #Noise (video) #Physics #Probability density function #Quantum mechanics #Spectral density #Statistical physics #Statistics #Turbulence #White noise #cond-mat.stat-mech #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/s10955-006-9116-9
published as J. Stat. Phys. 123, p909 (2006) · 13pages, 13 figures
openalex publication_date 2006/05/01 · arxiv created 2007/07/17 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 for a random noise with arbitrary power spectrum density and 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.