Related papers: Simple model for 1/f noise
We demonstrate that the measurement of $1/f^{\alpha}$ noise at the single molecule or nano-object limit is remarkably distinct from the macroscopic measurement over a large sample. The single particle measurements yield a conditional…
The problem of the intrinsic origin of 1/f noise is considered. Currents and signals consisting of a sequence of pulses are analysed. It is shown that intrinsic origin of 1/f noise is a random walk of the average time between subsequent…
The major goal of the present paper is to find out the manifestation of the boundedness of fluctuations. Two different subjects are considered: (i) an ergodic Markovian process associated with a new type of large scaled fluctuations at…
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…
We present analytical and numerical results of modeling of flows represented as the correlated non-Poissonian point process and as the Poissonian sequence of pulses of the different size. Both models may generate signals with the power-law…
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary…
It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by $\frac{1}{f^{\alpha}}$ noise with $1\leq\alpha\leq 2$. The system of…
We examine the mean first passage time for a particle driven by highly correlated Gaussian fluctuations to reach one or more predetermined boundaries. We discuss a numerical algorithm to generate power-law correlated fluctuations and apply…
Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron. In this…
We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous $1/f^2$ scaling within the power spectrum. We develop…
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…
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory,…
We study the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and L\"ocherbach (2016) in a diffusive scaling. The system consists of $N$ neurons, each spiking randomly with rate depending on its…
We investigate the generation of quantum operations for one-qubit systems under classical noise with 1/f^\alpha power spectrum, where 2>\alpha > 0. We present an efficient way to approximate the noise with a discrete multi-state Markovian…
Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise.…
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 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…
We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…
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)…
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…