  We develop a model of bistable oscillator with nonlinear dissipation. Using a
numerical simulation and an electronic circuit realization of this system we
study its response to additive noise excitations. We show that depending on
noise intensity the system undergoes multiple qualitative changes in the
structure of its steady-state probability density function (PDF). In
particular, the PDF exhibits two pitchfork bifurcations versus noise intensity,
which we describe using an effective potential and corresponding normal form of
the bifurcation. These stochastic effects are explained by the partition of the
phase space by the nullclines of the deterministic oscillator.
