  Populations of globally coupled identical maps subject to additive,
independent noise are studied in the regimes of strong coupling. Contrary to
each noisy population element, the mean field dynamics undergoes qualitative
changes when the noise strength is varied. In the limit of infinite population
size, these macroscopic bifurcations can be accounted for by a deterministic
system, where the mean-field, having the same dynamics of each uncoupled
element, is coupled with other order parameters. Different approximation
schemes are proposed for polynomial and exponential functions and their
validity discussed for logistic and excitable maps.
