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- Aleksei V. Chechkin, Joseph Klafter, Vsevolod Yu Gonchar, Ralf Metzler, Leonid V Tanatarov
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2003

We investigate the statistical behavior of LÃ©vy flights confined in a symmetric, quartic potential well U(x) proportional, variant x(4). At stationarity, the probability density function features a distinct bimodal shape and decays with power-law tails which are steep enough to give rise to a finite variance, in contrast to free LÃ©vy flights. From aâ€¦ (More)

- Krzysztof Burnecki, Agnieszka WyÅ‚omaÅ„ska, Aleksei Beletskii, Vsevolod Yu Gonchar, Aleksei V. Chechkin
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2012

We address the problem of recognizing Î±-stable LÃ©vy distribution with LÃ©vy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of the empirical probability density function is close to aâ€¦ (More)

- Aleksei V. Chechkin, Vsevolod Yu Gonchar, Rudolf Gorenflo, Nickolay Korabel, I. M. Sokolov
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2008

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R.â€¦ (More)

- Oleksii Yu Sliusarenko, Vsevolod Yu Gonchar, Aleksei V. Chechkin, I. M. Sokolov, Ralf Metzler
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2010

We investigate the escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the Hurst exponent H and the particle diffusivity D. We observeâ€¦ (More)

- Nickolay Korabel, R Klages, Aleksei V. Chechkin, I. M. Sokolov, Vsevolod Yu Gonchar
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2007

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random-walk theory well approximates the coarse behavior of this quantity in terms of a continuous function. Thisâ€¦ (More)

- Yu. L. Bolotin, Vsevolod Yu Gonchar, Andrei A. Krokhin, P H HernÃ¡ndez-Tejeda, A. V. Tur, Vladimir V. Yanovsky
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2001

We study the nonlinear dynamics of a complex system, described by a two-dimensional reversible map. The phase space of this map exhibits elements typical of Hamiltonian systems (stability islands) as well as of dissipative systems (attractor). Due to the interaction between the stability islands and the attractor, the transition to chaos in this systemâ€¦ (More)

- Aleksei V. Chechkin, Vsevolod Yu Gonchar, Joseph Klafter, Ralf Metzler
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

LÃ©vy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations LÃ©vy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to LÃ©vy noise can beâ€¦ (More)

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