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

Bronislovas Kaulakys; Julius Ruseckas; Vygintas Gontis; Miglius Alaburda

doi:10.1016/j.physa.2006.01.017

paper

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

arXiv:cond-mat/0509626 · doi:10.1016/j.physa.2006.01.017

Abstract

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^β $n o i se an d$ 1/x^λ $d i s t r ib u t i o n d e n s i t y o f t h es i g na l in t e n s i t y w i t h d i f f er e n t v a l u eso f$ β $an d$ λ $. T h e p r ocesses w i t h$ 1/f^β$ 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.

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