Eur. Phys. J. B (2016) 89: 64
https://doi.org/10.1140/epjb/e2016-60883-2

Regular Article

Dynamical continuous time random Lévy flights

¹ School of Science, Beijing Technology and Business University, Beijing 100048, P.R. China
² State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China

^a e-mail: liujian@mail.bnu.edu.cn

Received: 12 November 2015
Received in final form: 22 January 2016
Published online: 7 March 2016

Abstract

The Lévy flights’ diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton’s Second Law while the nonlinear friction f(v) = − γ₀v − γ₂v³ being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index μ = 2 case, it is still Brownian motion.