Rise and saturation of the correlation time near bifurcation threshold

A new non-linear fluctuation phenomenon is reported: prebifurcation rise of fluctuations' correlation time followed with saturation in the immediate vicinity of the bifurcation threshold. Analysis of the phenomenon is performed by the example of a period-doubling bifurcation in a noisy non-linear map. A linear theory is developed for the phenomenon under study and non-linear estimates are suggested for correlation time saturation in the very vicinity of the bifurcation point. It is shown, that correlation time saturates at the level inverse proportional to the noise standard deviation. Characteristic features of the phenomenon are illustrated by the results of numerical simulations