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
SN - 0301-0104
VL - 284
SP - 233
EP - 251
JO - Chemical Physics
JF - Chemical Physics
IS - 1-2
ER -