Low frequency noise controls on-off intermittency of bifurcating systems

TL;DR

This paper investigates how low-frequency noise influences on-off intermittency in bifurcating systems, revealing that reducing zero-frequency noise spectrum significantly diminishes intermittency and alters off-phase durations.

Contribution

It demonstrates the critical role of zero-frequency noise spectrum in controlling intermittency, providing a perturbative and numerical analysis of this effect in bifurcating systems.

Findings

Reducing zero-frequency noise spectrum shrinks the intermittency regime.

Intermittency is highly sensitive to the noise spectrum at zero frequency.

The distribution of off-phase durations is significantly affected by low-frequency noise control.

Abstract

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative expansion and numerical studies of the probability density function of the unstable mode, we show that intermittency is controlled by the ratio between the departure from onset and the value of the noise spectrum at zero frequency. Reducing the noise spectrum at zero frequency shrinks the intermittency regime drastically. This effect also modifies the distribution of the duration that the system spends in the off phase. Mechanisms and applications to more complex bifurcating systems are discussed.