TY - JOUR

T1 - Stationary states of non-linear oscillators driven by Lévy noise

AU - Chechkin, A.

AU - Gonchar, V.

AU - Klafter, J.

AU - Metzler, R.

AU - Tanatarov, L.

N1 - Funding Information:
The authors thank G. Voitsenya for help in numerical simulation, and R. Gorenflo, F. Mainardi and I. M. Sokolov for fruitful discussions. This work is supported by the INTAS Project 00-0847. RM acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG) within the Emmy Noether programme. AC acknowledges support from the DAAD.

PY - 2002/11/1

Y1 - 2002/11/1

N2 - We study the probability density function in the stationary state of non-linear oscillators which are subject to Lévy stable noise and confined within symmetric potentials of the general form U(x) ∝ x2m-2/(2m + 2), m = 0, 1,2,.... For m ≥ 1, the probability density functions display a distinct bimodal character and have power-law tails which decay faster than those of the noise probability density. This is in contrast to the Lévy harmonic oscillator m = 0. For the particular case of an anharmonic Lévy oscillator with U(x) = ax2/2+bx4/4, a > 0, we find a turnover from unimodality to bimodality at stationarity.

AB - We study the probability density function in the stationary state of non-linear oscillators which are subject to Lévy stable noise and confined within symmetric potentials of the general form U(x) ∝ x2m-2/(2m + 2), m = 0, 1,2,.... For m ≥ 1, the probability density functions display a distinct bimodal character and have power-law tails which decay faster than those of the noise probability density. This is in contrast to the Lévy harmonic oscillator m = 0. For the particular case of an anharmonic Lévy oscillator with U(x) = ax2/2+bx4/4, a > 0, we find a turnover from unimodality to bimodality at stationarity.

KW - Fractional derivative

KW - Fractional kinetic equation

KW - Lévy flights

KW - Lévy stable noise

KW - Non-linear oscillator

UR - http://www.scopus.com/inward/record.url?scp=0036830088&partnerID=8YFLogxK

U2 - 10.1016/S0301-0104(02)00551-7

DO - 10.1016/S0301-0104(02)00551-7

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AN - SCOPUS:0036830088

VL - 284

SP - 233

EP - 251

JO - Chemical Physics

JF - Chemical Physics

SN - 0301-0104

IS - 1-2

ER -