Spectral Broadening of Period-Doubling Bifurcation Sequences

Abstract

A perturbation calculation shows that the power spectrum of strange attractor near the accumulation parameter of a period-doubling bifurcation sequence consists of peaks broadened by a phase modulation, with broad skirts created by an amplitude modulation. Moving toward the accumulation parameter, at each bifurcation the total noise power decreases by a factor of 10.48, the average peak width decreases by a factor of 20.96, and the spectral bandwidth of the skirts decreases by a factor of 2.