Stellar activity is notoriously difficult to model, being neither periodic nor purely stochastic. In light curves, the interplay between the stellar rotation period and the birth and death of spots and faculae gives rise to quasi-periodic modulation over time scales of hours to weeks. Despite the complexity of this interplay, the resulting light curves bear strong qualitative resemblance to systems known to exhibit low-dimensional dynamical chaos, such as the Rössler attractor.
In the 1980s and 1990s, a suite of techniques for nonlinear dynamical analysis, called attractor reconstruction, evolved to study exactly this type of system. Attractor reconstruction works by embedding a 1-dimensional time series, such as stellar light curve, in a higher-dimensional phase space capable of capturing its full dynamical behavior: too low a dimensionality, and the system's trajectory will self-intersect and tangle, which we know to be physically unrealistic given the non-periodicity of the observed signal. This technique has been used successfully to model the historical sunspot record and the light curves of variable stars (both simulated and observed) and to recover important features of their underlying dynamics, including their dimensionality and the time scales over which they can be meaningfully forecast into the future. Here, I discuss the application of attractor reconstruction to the light curves of active main-sequence stars observed by Kepler, TESS, and ground-based surveys.