Starting from the developed generalized point process model of 1/f noise [B. Kaulakys et al., Phys. Rev. E 71 (2005) 051105] we derive the nonlinear stochastic differential equations for the signal exhibiting 1/fβ noise and 1/xλ distribution density of the signal intensity with different...

Power-law distributions have been observed in various economical and physical systems. Lévy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the “gradually truncated Lévy flight” in which large steps of a Lévy flight are...

We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a nontrivial stationary state. We discuss the results and...

We study numerically the phase behaviour in two different arrays of overdamped bistable oscillators coupled unidirectionally, each of them fed by an external source of Gaussian white noise, and driven by an external periodic force.

Arrival times of requests to print in a student laboratory were analyzed. Inter-arrival times between subsequent requests follow a universal scaling law relating time intervals and the size of the request, indicating a scale invariant dynamics with respect to the size. The cumulative...

We report new results about the two-time dynamics of an anomalously diffusing classical particle, as described by the generalized Langevin equation with a frequency-dependent noise and the associated friction. The noise is defined by its spectral density proportional to ωδ−1 at low...

We analyze in detail how the anomalous drift and diffusion properties of a particle evolving in an aging medium can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility...

We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to |ω|δ−1 at small frequencies, with...