Coupled nonlinear stochastic differential equations generating arbitrary distributed observable with 1/f noise. (19th April 2016) - Ruseckas, J; Kazakevičius, R; Kaulakys, B
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 β 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 allow us to obtain a 1 / f β spectrum in a wide range of frequencies together with the almost arbitrary steady-state density of the signal.