Volume 111, Number 5, September 2015
|Number of page(s)||6|
|Published online||18 September 2015|
Power-law distributions in noisy dynamical systems
1 Department of Mathematics and Statistics, The Open University - Walton Hall, Milton Keynes, MK7 6AA, England, UK
2 Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, Université de Lyon F-69007, Lyon, France
3 Max-Planck Institute for Dynamics and Self-Organisation - D-37077, Göttingen, Germany
Received: 11 May 2015
Accepted: 19 August 2015
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.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.Df – Fractals
© EPLA, 2015
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