Effects of the low frequencies of noise on On-Off intermittency

TL;DR

This paper investigates how low-frequency noise influences on-off intermittency in bifurcating systems, deriving analytical results and confirming them through numerical simulations with different noise types.

Contribution

It provides a detailed analysis of the dependence of on-off intermittency on the noise power spectrum, including analytical derivations and extensions to complex systems.

Findings

Intermittency depends on the ratio of threshold departure to noise PSD at zero frequency.

Analytical results agree with numerical simulations using Gaussian and chaotic noise.

The study extends understanding of noise effects on bifurcating systems.

Abstract

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.