Abstract

Our system has been thoroughly studied and demonstrated to show the Feigenbaum period doubling route to chaos. We have extended the study of such a system by applying an external signal and observing both experimentally and numerically its effects. One such effect is modal amplification, amplification of the external signal at frequencies which coincide with the natural frequencies or modes of the system. This is observed before both Hopf and period doubling bifurcations. Normally the first mode determines the system’s behavior, but when a signal at the same frequency as a higher-order mode is applied the system can be made to oscillate in this mode. Once the system has bifurcated to a periodic solution it is possible, if the amplitude and frequencies are properly chosen, to fix the frequency of oscillation of the system at that of the external signal. Even when the system shows chaotic behavior, certain modulation frequencies force the system to become periodic. The frequency spectrum both before and after a bifurcation exhibits an effect, called candelabra, or the presence of many additional lines in the spectrum.

© 1987 Optical Society of America