Power-law distributions in noisy dynamical systems

Wilkinson, Michael; Guicharaz, Robin; Pradas, Marc and Pumir, Alain (2015). Power-law distributions in noisy dynamical systems. EPL, 111(5), article no. 50005.

DOI: https://doi.org/10.1209/0295-5075/111/50005


We consider a dynamical system which is non-autonomous, has a stable attractor and which is perturbed by an additive noise. We establish that under some quite typical conditions, the intermittent fluctuations from the attractor 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, and is explicitly determined, using numerics or perturbation expansion, in the case of a model of colloidal particles in one-dimension.

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