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.