Journal of Statistical Physics, Vol. 43, Nos. 1/2, 1986. p. 349-368.
The average trajectories and fluctuations around them resulting from an ensemble of noisy, nonlinear maps are analyzed. The bifurcation diagram for the average value obtained from the computer simulation of noisy maps ensemble is discussed first. Then a deterministic average equation of motion describing in an approximate way the time evolution of the average value and of the variance is analyzed numerically. This equation predicts the existence of the bifurcation gap and of the exceptional attractors for special initial points. The scaling properties of the average value and of the variance are obtained with the help of this equation.