Phase-sensitive amplification and deamplification of noise and the noise rise in period-doubling systems near a bifurcation

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Abstract
We have observed in experiments with a driven nonlinear electrical resonator that the fluctuations in the ‘‘noisy precursor’’ to a period-doubling bifurcation are phase dependent and that the noise is deamplified in one of the phases. This is a classical effect analogous to ‘‘squeezing’’ which normally refers to deamplification of quantum noise. Preceding the period-doubling bifurcation a ‘‘noise rise’’ similar to that observed in Josephson-junction parametric amplifiers evolves and the noise deamplification ceases. This phenomenon and the ‘‘noise rise’’ appear to be related as successive stages in the development of bifurcation in a nonlinear system in the presence of noise.