  For a model nonlinear dynamical system, we show how one may obtain its
bifurcation behavior by introducing noise into the dynamics and then studying
the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to
capture the bifurcation behavior in the noisy dynamics is the conditional
probability to observe a microscopic configuration at one time, conditioned on
the observation of a given configuration at an earlier time. For our model
system, this conditional probability is studied by using two complementary
approaches, the Fokker-Planck and the path-integral approach. The latter has
the advantage of yielding exact closed-form expressions for the conditional
probability. All our predictions are in excellent agreement with direct
numerical integration of the dynamical equations of motion.
