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 α-stable Lévy 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 solving a nonlocal Fokker-Planck equation numerically.This allows numerically investigating phenomenological bifurcation,or P-bifurcation,for stochastic differential equations with non-Gaussian Lévy noises.