Nonlinear stochastic models of 1/f noise and power-law distributions

Details Nonlinear stochastic models of 1/f noise and power-law distributions Nonlinear stochastic models of 1/f noise and power-law distributions

2005-09-24

arxiv.org/abs/cond-mat/0509626v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, 6 figures, presented at the 3rd NEXT-SigmaPhi International Conference (13-18 August 2005, Kolymbari CRETE)

Scientific paper

10.1016/j.physa.2006.01.017

Starting from the developed generalized point process model of $1/f$ noise (B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive the nonlinear stochastic differential equations for the signal exhibiting 1/f^{\beta}$ noise and $1/x^{\lambda}$ distribution density of the signal intensity with different values of $\beta$ and $\lambda$. The processes with $1/f^{\beta}$ are demonstrated by the numerical solution of the derived equations with the appropriate restriction of the diffusion of the signal in some finite interval. The proposed consideration may be used for modeling and analysis of stochastic processes in different systems with the power-law distributions, long-range memory or with the elements of self-organization.

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