  We study stochastic bifurcation for a system under multiplicative stable Levy
noise (an important class of non-Gaussian noise), by examining the qualitative
changes of equilibrium states in its most probable phase portraits. We have
found some peculiar bifurcation phenomena in contrast to the deterministic
counterpart: (i) When the non-Gaussianity parameter in Levy noise varies, there
is either one, two or none backward pitchfork type bifurcations; (ii) When a
parameter in the vector field varies, there are two or three forward pitchfork
bifurcations; (iii) The non-Gaussian Levy noise clearly leads to fundamentally
more complex bifurcation scenarios, since in the special case of Gaussian
noise, there is only one pitchfork bifurcation which is reminiscent of the
deterministic situation.
