  Nonlinear dynamical systems are sometimes under the influence of random
fluctuations. It is desirable to examine possible bifurcations for stochastic
dynamical systems when a parameter varies.
  A computational analysis is conducted to investigate bifurcations of a simple
dynamical system under non-Gaussian {\alpha}-stable Levy motions, by examining
the changes in stationary probability density functions for the solution orbits
of this stochastic system. The stationary probability density functions are
obtained by numerically solving a non local Fokker-Planck equation. This allows
numerically investigating phenomenological bifurcation, or
  P-bifurcation, for stochastic differential equations with non-Gaussian Levy
noises.
