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We introduce a relaxation algorithm to estimate approximations to generating partitions for observed dynamical time series. Generating partitions preserve dynamical information of a deterministic map in the symbolic representation. Our method optimizes an essential property of a generating partition: avoiding topological degeneracies. We construct an(More)
A symbolic analysis of observed time series requires a discrete partition of a continuous state space containing the dynamics. A particular kind of partition, called "generating," preserves all deterministic dynamical information in the symbolic representation, but such partitions are not obvious beyond one dimension. Existing methods to find them require(More)
The synchronization of chaotic rare-earth-doped fiber ring lasers is analyzed. The lasers are first coupled by transmitting a fraction c of the circulating electric field in the transmitter and injecting it into the optical cavity of the receiver. A coupling strategy which relies on modulation of the intensity of the light alone is also examined.(More)
The unstable periodic orbits of a chaotic system provide an important skeleton of the dynamics in a chaotic system, but they can be difficult to find from an observed time series. We present a global method for finding periodic orbits based on their symbolic dynamics, which is made possible by several recent methods to find good partitions for symbolic(More)