title: Bifurcation, bimodality, and finite variance in confined Lévy flights.
abstract: We investigate the statistical behavior of Lévy 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 Lévy flights. From a delta-initial condition, a bifurcation of the unimodal state is observed at t(c)>0. The nonlinear oscillator with potential U(x)=ax(2)/2+bx(4)/4, a,b>0, shows a crossover from unimodal to bimodal behavior at stationarity, depending on the ratio a/b.
authors.affiliation: Institute for Theoretical Physics NSC KIPT, Akademicheskaya Street 1, 61108 Kharkov, Ukraine.
authors.forename: Aleksei V
authors.initials: AV
authors.lastname: Chechkin
authors.forename: Joseph
authors.initials: J
authors.lastname: Klafter
authors.forename: Vsevolod Yu
authors.initials: VY
authors.lastname: Gonchar
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler
authors.forename: Leonid V
authors.initials: LV
authors.lastname: Tanatarov