Related papers: Levy ratchets with dichotomic random flashing
We propose a threshold detector for L\'evy distributed fluctuations based on a Josephson junction. The L\'evy noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…
We focus in this paper on the stochastic stabilization problems of PDEs by Levy noise. Sufficient conditions under which the perturbed systems decay exponentially with a general rate function are provided and some examples are constructed…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
We report measurements and analysis of the voltage noise due the to vortex motion, performed in superconducting Niobium micro-bridges. Noise in such small systems exhibits important changes from the behavior commonly reported in macroscopic…
When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and…
The blow-up phenomena of stochastic semilinear parabolic equations with additive as well as linear multiplicative L\'evy noises are investigated in this work. By suitably modifying the concavity method in the stochastic context, we…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power--law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the…
We study the phenomena of noise induced transport in frictional ratchet systems. For this we consider a Brownian particle moving in a space dependent frictional medium in the presence of external white noise fluctuations. To get the…
The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is…
Studies of noise-induced motions are showing that coherent energy can be extracted from some kinds of noise in a periodic ratchet. Recently, energetics of Langevin dynamics is formulated by Sekimoto [J.Phys.Soc.Jpn, 66 1234 (1997)], which…
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…
We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent…
We generalise the Langevin equation with Gaussian white noise by replacing the velocity term by a local fractional derivative. The solution of this equation is a Levy process. We further consider the Brownian motion of a fractal particle,…