TY - JOUR
T1 - Bifurcation, bimodality, and finite variance in confined Lévy flights
AU - Chechkin, Aleksei V.
AU - Klafter, Joseph
AU - Gonchar, Vsevolod Yu
AU - Metzler, Ralf
AU - Tanatarov, Leonid V.
PY - 2003
Y1 - 2003
N2 - We investigate the statistical behavior of Lévy flights confined in a symmetric, quartic potential well [Formula presented] 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 Lévy flights. From a δ-initial condition, a bifurcation of the unimodal state is observed at [Formula presented] The nonlinear oscillator with potential [Formula Presented] shows a crossover from unimodal to bimodal behavior at stationarity, depending on the ratio [Formula presented]
AB - We investigate the statistical behavior of Lévy flights confined in a symmetric, quartic potential well [Formula presented] 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 Lévy flights. From a δ-initial condition, a bifurcation of the unimodal state is observed at [Formula presented] The nonlinear oscillator with potential [Formula Presented] shows a crossover from unimodal to bimodal behavior at stationarity, depending on the ratio [Formula presented]
UR - http://www.scopus.com/inward/record.url?scp=85035275832&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.67.010102
DO - 10.1103/PhysRevE.67.010102
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AN - SCOPUS:85035275832
SN - 1063-651X
VL - 67
SP - 4
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 1
ER -