Related papers: 1/f noise from the nonlinear transformations of th…
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}$…
We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of…
We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f fluctuations in the simple systems affected by the external random perturbations, i.e. the power spectral density of the flux of particles moving…
There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We…
We present and analyze the simple analytically solvable model of 1/f noise, which can be relevant for the understanding of the origin, main properties and parameter dependencies of the flicker noise. In the model, the currents or signals…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
We consider stochastic model based on the linear stochastic differential equation with the linear relaxation and with the diffusion-like fluctuations of the relaxation rate. The model generates monofractal signals with the non-Gaussian…
We provide evidence that for some values of the parameters a simple agent based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of…
An approach to the problem of 1/f voltage noise observed in all conducting media is developed based on an uncertainty relation for the Fourier-transformed signal. It is shown that the quantum indeterminacy caused by non-commutativity of…
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…
Noise of stochastic processes whose power spectrum scales at low frequencies, $f$, as $1/f$ appears in such diverse systems that it is considered universal. However, there have been a small number of instances from completely unrelated…
Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…
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…
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation)…
This report is aimed at reviving the explanation of flicker-noise observations as the result of spectral measurement of very low-frequency but stationary narrow-band fluctuations named as infralow-frequency noise (ILF noise) [A. Ya.…
Discovering the mechanism underlying the ubiquity of $"1/f^{\alpha}"$ noise has been a long--standing problem. The wide range of systems in which the fluctuations show the implied long--time correlations suggests the existence of some…
Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an…
The power spectrum of quantum dot fluorescence exhibits $1/f^\beta$ noise, related to the intermittency of these nanosystems. As in other systems exhibiting $1/f$ noise, this power spectrum is not integrable at low frequencies, which…
The collective behavior of a two-dimensional wet granular cluster under horizontal swirling motions is investigated experimentally. Depending on the balance between the energy injection and dissipation, the cluster evolves into various…
We present a simple stochastic mechanism which generates pulse trains exhibiting a power law distribution of the pulse intervals and a $1/f^\alpha$ power spectrum over several decades at low frequencies with $\alpha$ close to one. The…