1/<i>f</i>noise from point process and time-subordinated Langevin equations

Ruseckas, Julius; Kazakevičius, Rytis; Kaulakys, B.

doi:10.1088/1742-5468/2016/05/054022

Cited by 12 publications

(18 citation statements)

References 61 publications

(130 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The powerlaw form of the coefficients in SDE (10) allows us to introduce an operational time τ in addition to the physical time t so that the diffusion coefficient in the operational time becomes constant [65]. The relation between the physical time t and the operational time τ is specified by the equation dt = σ −2 x −2η dτ .…”

Section: External Force That Does Not Limit the Anomalous Diffusionmentioning

confidence: 99%

Influence of external potentials on heterogeneous diffusion processes

Kazakevičius

Ruseckas

2017

2017 International Conference on Noise and Fluctuations (ICNF)

View full text Add to dashboard Cite

In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. The heterogeneous diffusion processes can yield subdiffusion as well as superdiffusion, depending on the behavior of the diffusion coefficient. We assume that not only the diffusion coefficient but also the external force has a power-law dependence on the position. We obtain analytic expressions for the transition probability in two cases: when the power-law exponent in the external force is equal to 2η − 1, where 2η is the power-law exponent in the dependence of the diffusion coefficient on the position, and when the external force has a linear dependence on the position. We found that the power-law exponent in the dependence of the mean square displacement on time does not depend on the external force, this force changes only the anomalous diffusion coefficient. In addition, the external force having the power-law exponent different from 2η − 1 limits the time interval where the anomalous diffusion occurs. We expect that the results obtained in this paper may be relevant for a more complete understanding of anomalous diffusion processes.

show abstract

Section: External Force That Does Not Limit the Anomalous Diffusionmentioning

confidence: 99%

Influence of external potentials on heterogeneous diffusion processes

Kazakevičius

Ruseckas

2017

2017 International Conference on Noise and Fluctuations (ICNF)

View full text Add to dashboard Cite

show abstract

“…The numerical solution scheme can by improved by using a variable time step that becomes small only when y becomes large. Such method of solution of a single nonlinear SDE has been proposed in [35,46]. The variable time step is equivalent to the introduction of the internal time τ that is different from the real, physical, time t [46].…”

Section: Numerical Approachmentioning

confidence: 99%

“…Such method of solution of a single nonlinear SDE has been proposed in [35,46]. The variable time step is equivalent to the introduction of the internal time τ that is different from the real, physical, time t [46]. In order to make the solution more efficient we introduce an internal, operational, time τ by the equation…”

Section: Numerical Approachmentioning

confidence: 99%

“…Since y t > 0, from equation (34) it follows that τ t is a strictly increasing function of time t. Let us obtain the SDEs for the stochastic variables x and y in the internal time τ . To do this we proceed similarly as in [46] and consider the joint PDF P x,y,τ (x, y, τ ; t) of the stochastic variables x, y and τ . The PDF P (x, y; t) can be calculated using the equation…”

Section: Numerical Approachmentioning

confidence: 99%

“…However, the actual signal changes according to SDE (45), the periods of fast fluctuations are similar to the periods of slow fluctuations compressed in time. Analysis of nonlinear SDEs similar to (46), performed in [14], reveals that the sizes of the bursts are approximately proportional to the squared durations of the bursts. The distributions of burst and inter-burst durations have power-law parts, with the numerically estimated power-law exponent of the PDF of the inter-burst durations approximately equal to −3/2.…”

Section: Numerical Approachmentioning

confidence: 99%

See 2 more Smart Citations

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

Ruseckas¹,

Kazakevičius²,

Kaulakys

2016

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

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 allows us to obtain 1/f β spectrum in a wide range of frequencies together with the almost arbitrary steady-state density of the signal.

show abstract