The correlated Levy flight is studied analytically in terms of the fractional Fokker-Planck equation and simulated numerically by using the Langevin equation, where the usual white Ltvy noise is generalized to an Orns...The correlated Levy flight is studied analytically in terms of the fractional Fokker-Planck equation and simulated numerically by using the Langevin equation, where the usual white Ltvy noise is generalized to an Ornstein-Uhlenbeck Levy process （OALP） with a correlation time τc. We analyze firstly the stable behavior of OULP. The probability density function of Ltvy flight particle driven by the OULP in a harmonic potential is exactly obtained, which is also a Ltvy-type one with Tc-dependence width; when the particle is bounded by a quartic potential, its stationary distribution has a bimodality shape and becomes noticeable with the increase of τc.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61178067,10875013 and 11175021)the Doctoral Scientific Research Starting Foundation of Taiyuan University of Science and Technology(Grant No.20122042)
文摘The correlated Levy flight is studied analytically in terms of the fractional Fokker-Planck equation and simulated numerically by using the Langevin equation, where the usual white Ltvy noise is generalized to an Ornstein-Uhlenbeck Levy process （OALP） with a correlation time τc. We analyze firstly the stable behavior of OULP. The probability density function of Ltvy flight particle driven by the OULP in a harmonic potential is exactly obtained, which is also a Ltvy-type one with Tc-dependence width; when the particle is bounded by a quartic potential, its stationary distribution has a bimodality shape and becomes noticeable with the increase of τc.
