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arXiv · 1603.03013

Coupled nonlinear stochastic differential equations generating arbitrary distributed observable with 1/f noise

J. Ruseckas·R Kazakevičius·B Kaulakys
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Abstract

Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the signal. In this paper we generalize this model and propose a system of two coupled nonlinear stochastic differential equations. The equations are derived from the scaling properties necessary for the achievement of 1/f noise. The first equation describes the changes of the signal, whereas the second equation represents a fluctuating rate of change. The proposed coupled stochastic differential equations allows us to obtain 1/f spectrum in a wide range of frequencies together with the almost arbitrary steady-state density of the signal.

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J. Ruseckas, R Kazakevičius, B Kaulakys. 2016-03-09. Coupled nonlinear stochastic differential equations generating arbitrary distributed observable with 1/f noise. https://doi.org/10.1088/1742-5468/2016/04/043209

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