Experimental phase synchronization of chaos in a plasma discharge is studied using a phase variable lift technique (i.e., phase points separated by 2pi are not considered as the same). Real-time observation of synchronized and unsynchronized states is made possible through a real-time sampling procedure. Parameter space regions of synchronization and unsynchronization are identified, and a set of equations is suggested to model the real plasma circuit.

Experimental phase synchronization of chaos is demonstrated for a plasma discharge tube subject to a high dc voltage (800-900 V), and paced with a low amplitude (less than 1 V) wave generator.

We characterize the Rössler system by means of a map associating colors to various intervals of largest Lyapunov exponent values in parameter space. This color map allows quick access to quantitative information about the dynamics of the system. The map also permits parameter space navigation while intentionally maintaining the system in a desired state, and avoiding regions where the system's behavior would be undesirable. In addition, the map exhibits a rich structure of stability clusters composed of affine-similar repetitions of basic elementary cells called "swallows." These cells, until recently, have been known to be associated with discrete maps only.

Experimental phase synchronization of chaos is demonstrated for two different chaotic oscillators: a plasma discharge and the Chua circuit. Our technique includes real-time capability for observing synchronization-desynchronization transitions. This capability results from a strong combination of synchronization and control, and allows tuning adjustments for search and stabilization of synchronous states. A power law is observed for the mean time between 2pi phase slips for different coupling strenghts. The experimental results are consistent with the numerical simulations.

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