A. A. Dubkov

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We show that the increments of generalized Wiener process, useful to describe nonGaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov’s equation for(More)
The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We(More)
The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise(More)
The noise can stabilize a fluctuating or a periodically driven metastable state in such a way that the system remains in this state for a longer time than in the absence of white noise. This is the noise enhanced stability phenomenon, observed experimentally and numerically in different physical systems. After shortly reviewing all the physical systems(More)
A. A. Dubkov, B. Spagnolo, and V. V. Uchaikin ♯ Radiophysics Faculty, Nizhniy Novgorod State University 23 Gagarin Ave., 603950 Nizhniy Novgorod, Russia∗ ⋆ Dipartimento di Fisica e Tecnologie Relative and CNISM-INFM, Group of Interdisciplinary Physics†, Università di Palermo, Viale delle Scienze, I-90128, Palermo, Italy‡ and ♭ Department of Theoretical(More)
We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise(More)
We investigate the overdamped Brownian motion in a supersymmetric periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ from each other by a shift of one-half period. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general(More)
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Lévy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density function of Lévy flights in different smooth potential profiles. We find confinement of the particle in the(More)
The stability of a simple dynamical system subject to multiplicative one-side pulse noise with hidden periodicity is investigated both analytically and numerically. The stability analysis is based on the exact result for the characteristic functional of the renewal pulse process. The influence of the memory effects on the stability condition is analyzed for(More)
We consider a Lotka-Volterra system of two competing species subject to multiplicative α-stable Lévy noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive α-stable Lévy noise. We study the(More)