  This paper numerically investigates the mean first passage time (MFPT) and
phase transition of a bistable Duffing system driven by L\'evy stable noise,
which can reduce to the common Gaussian noise with the stability index 2. We
obtain the stationary probability density functions by using Monte Carlo method
to describe the change in distribution law and the influences of L\'evy noise
parameters on the stationary probability densities are discussed. The results
indicate that the stability index, noise intensity and skewness parameter of
L\'evy noise can induce the phase transition behaviors (namely, the qualitative
change of stationary probability density function). Furthermore, the MFPT is
calculated as functions of different parameters, which implies that the effects
of the stability index, noise intensity and the skewness parameter on MFPT are
quite different, and apparent distinctions between L\'evy and Gaussian noise
can be observed.
