Transient statistics in stabilizing periodic orbits

Abstract

The statistics of chaotic and periodic transient time intervals preceding the stabilization of a given periodic orbit have been experimentally studied in a ${\mathrm{CO}}_{2}$ laser with modulated losses, subjected to a small subharmonic perturbation. As predicted by the theory, an exponential tail has been found in the probability distribution of chaotic transients. Furthermore, a fine periodic structure in the distributions of the periodic transients, resulting from the interaction of the control signal and the local structure of the chaotic attractor, has been revealed.