Higher-order bifurcations in a bistable system with delay

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Abstract
The output intensity of a hybrid bistable system with a delay in the feedback loop is known to undergo regular and irregular self-pulsing. With the help of high-resolution power spectra, we have analyzed numerically the transition of this system into chaos for several different values of the delay time, and found evidence for the existence of an infinite sequence of period-doubling bifurcations, followed by a reverse sequence in which the periodic components of the spectrum are superimposed to a continuous noisy structure. We have studied the effect of external Gaussian random noise and verified, as expected, the occurrence of bifurcation gaps. In the vicinity of the self-pulsing threshold, more than three independent frequency components coexist without evidence for the appearance of a strange attractor.