Noise and bifurcations

The influence of while noise on bifurcating dynamical systems is investigated using both Fokker-Planck and functional integral methods. Noise leads to fuzzy bifurcations where physically relevant quantities become smooth functions of the bifurcation parameters. We study dynamical and probabilistic quantities, such as invariant measures, Liapunov exponents, correlation functions, and exit times. The behavior of these quantities near the deterministic bifurcation point changes for distinct values of the control parameter. Therefore the very concept of bifurcation point becomes meaningless and must be replaced by the notion of bifurcation region.