Stationary states of non-linear oscillators driven by Levy noise

We study the probability density function in the stationary state of non-linear oscillators which are subject to Levy stable noise and confined within symmetric potentials of the general form U(x) alpha x(2m+2)/(2m + 2), m = 0, 1, 2,.... For m greater than or equal to 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 Levy harmonic oscillator m = 0. For the particular case of an anharmonic Levy oscillator with U(x) = ax(2)/2 + bx(4)/4, a > 0, we find a turnover from unimodality to bimodality at stationarity. (C) 2002 Elsevier Science B.V. All rights reserved.