Nonlinear analysis of the light curve of the variable star R Scuti

It is first shown that the observational light curve data of R Scuti, a star of the RV Tau type, is not multiperiodic and that it cannot have been generated by a linear stochastic (AR) process. By default, the signal must be a manifestation of deterministic chaos. We use a novel nonlinear time series analysis, the global flow reconstruction technique, to probe the properties of the irregular pulsation cycles. We show in particular that the chaotic dynamics of this star's complicated light curve is captured by a simple four-dimensional polynomial map or flow (four first-order ordinary differential equations). Another important feature is that the method allows us to quantify an irregular signal that has the potential benefit for extracting novel stellar constraints from an irregular light curve. Finally, from the low dimensionality (four) of the flow we can infer a simple physical picture of the pulsations, and arguments are presented that the pulsations of R Sct are the result of the nonlinear interaction of two vibrational normal modes of the star.