Stationary states of non-linear oscillators driven by Lévy noise

A. Chechkin*, V. Gonchar, J. Klafter, R. Metzler, L. Tanatarov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)233-251
Number of pages19
JournalChemical Physics
Issue number1-2
StatePublished - 1 Nov 2002


  • Fractional derivative
  • Fractional kinetic equation
  • Lévy flights
  • Lévy stable noise
  • Non-linear oscillator


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