CONTROLLING CHAOS IN A FAST DIODE RESONATOR USING EXTENDED TIME-DELAYAUTOSYNCHRONIZATION - EXPERIMENTAL-OBSERVATIONS AND THEORETICAL-ANALYSIS

We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz (corresponding to a drive period under 100 ns) using exte nded time-delay autosynchronization. Stabilization is achieved by feed back of an error signal that is proportional to the difference between the value of a slate variable and an infinite series of values of the stale variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it h as an all-optical counterpart that may be useful for stabilizing the d ynamics of fast chaotic lasers. We show that increasing the weights gi ven to temporally distant states enlarges the domain of control and re duces the sensitivity of the domain of control on the propagation dela ys in the feedback loop. We determine the average time to obtain contr ol as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in th e presence of time-delay feedback is in good agreement with the experi mental results for the size and shape of the domain of control. (C) 19 97 American Institute of Physics.