Topological time-series analysis of a string experiment and its synchronized model

We identify the template organizing the chaotic dynamics of a vibrating string and show how to estimate topological parameter values directly from an experimental time series. We call these data processing techniques topological time-series analysis.'' The chaotic motions of a vibrating string are shown to be governed by a dissipative horseshoe map whose periodic orbit spectrum is, at the topological level, well described by a unimodal map of the interval. In addition, close topological agreement is demonstrated between the experimental data and a synchronized model. The empirical model of the experimental data allows us to create synthetic data.'' Such synthetic data may enable finer characterization of the system than that determined from the seed data alone.