Stochastic Cascade Amplification of Fluctuations

TL;DR

This paper investigates how additive noise causes intermittent fluctuations with power-law tails in stable dynamical systems, attributing this to a stochastic cascade mechanism that amplifies fluctuations during transient instabilities.

Contribution

It introduces a novel explanation for power-law fluctuations in noisy systems, linking them to a stochastic cascade process and interpreting the power-law exponent as a negative fractal dimension.

Findings

Fluctuations exhibit power-law tails due to stochastic cascade amplification.

Transient instability periods are key to fluctuation amplification.

Power-law exponent relates to a negative fractal dimension.

Abstract

We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with power-law tails. We show that this results from a stochastic cascade of amplification of fluctuations due to transient periods of instability. The exponent of the power-law is interpreted as a negative fractal dimension.