Successive Higher-Harmonic Bifurcations in Systems with Delayed Feedback

The scheme of bifurcations in systems described by a certain class of delay-differential equations is investigated in detail. It is shown that higher-harmonic oscillating states appear successively in the course of transition to developed chaos. First-order transitions between these states account for the frequency-locked anomaly recently observed by Hopf et al. in a hybrid optical bistable device. Among dynamical systems capable of displaying chaotic behavior, systems with delayed feedback are of interest since their time evolution is determined by a concurrence of a discrete step which tends to induce chaos and a continuous step which tends to smear it. A physical example of such systems is an optical cavity filled with a non-linear dielectric medium and irradiated with a laser light of constant intensity.